Debate On The Theory Of Relativity

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“The mechanics of
Newton, like the geom-
etry of Euclid, was based
upon our normal intui-
tions and it is, therefore,
intelligible in the normal
sense of the word, just
as Euclid is intelligible.”

“Einstein has given
us signs in the heavens
to corroborate his theory
and mankind will never
go back on signs in the
heavens.”

(Copyright Underwood &
Underwood.)

A Debate

on

The Theory of Relativity

WITH AN INTRODUCTION

By

WILLIAM LOWE BRYAN

President of Indiana University

Favoring the Theory :

Robert D. Carmichael,
Professor of Mathematics,
University of Illinois.

Harold T. Davis,
Assistant Professor of Mathematics,
Indiana University.

Opposing the Theory.

William D. MacMillan,

Professor of Astronomy,
University of Chicago.

Mason E. Hufford,
Assistant Professor of Physics,
Indiana University.

CHICAGO LOMDON

THE OPEN COURT PUBLISHING CO.

1927 .

Copyright by

The Open- Court Publishing Co

1927

Printed in America,

THE OCCASION

The debate on relativity contained in this volume
was held at Indiana University on May 21 and 22, 1926,
under the auspices of the Indiana chapter of Sigma Xi,
Because of the profound influence that this new doc-
trine has already had upon philosophic thought and
the attention it has directed to the foundations of
mathematical physics, it is important that the most
careful scrutiny should be given to the postulates which
underlie it and to the experimental evidence upon which
it rests. Recently the work of Professor Dayton C.
Miller has threatened the experimental foundations of
the theory and a reasonable doubt as to its validity has
been entertained by a group of scientific men.

In order to give an opportunity for the presenta-
tion of evidence on both sides of this important ques-
tion the Indiana Chapter of Sigma Xi extended an
invitation to two mathematicians, an astronomer, and
a physicist to debate the question. The result is con-
tained in the present volume.

The meetings were presided over by Professor
William M. Tucker, president of the local chapter of
Sigma Xi, and the introductory address was made by
President William Lowe Bryan. On the second even-
ing Professor John B. Dutcher of the Physics depart-
ment projected interference fringes upon a screen in
order to give those present some notion of the delicate
and treacherous phenomena whose study has been fun-
damental in the erection of the new theory.

CONTENTS.

PAGE

Introduction vii

The Foundation Principles of Relativity,

The Opening Arguments of the Affirmative

Professor R. D. Carmichael ... 1

The Postulates of Normal Intuition.

The First Speech of the Negative

Professor W. D. MacMillan ... 39

Is the Experimental Evidence of Relativity
Conclusive ?

The Second Speech of the Negative

Professor M. E. Hufford . ... 64

The Experimental Verification of Relativity.

Concluding Arguments of the Affirmative

Professor H. T. Davis 90

The Fourth Doctrine of Science and its Limi-
tations.

The Rebuttal of the Negative

Professor W. D, MacMillan . . . 117

Philosophical Implications of the Theory.

The Final Rejoinder of the Affirmative

Professor R. D. Carmichael .... 128

Index 151

INTRODUCTION

It has been said that men fall into three classes ac-
cording to their underlying assumption as to the nature
of reality. The first class, which includes most of man-
kind, assumes that reality is static; the second that
nothing is static but all things in eternal flux; the
third that throughout the eternal flux there is every-
where and always intelligible reason. The three class-
es of men take these three attitudes toward the sys-
tems of human knowledge: The first class holds that
certain systems of knowledge are the truth and are per-
manently valid ; the second that no knowledge is per-
manently valid and that the truth can never be known ;
the third that throughout the incessant change in every
minor and major part of human knowledge, reason
survives and becomes always more apparent and more
dependable for the guidance of conduct. Those who
have the first view are alarmed at every major change
in the system of science. Those who have the second
view regard such changes as cumulative justification
for skepticism as to the possibility of any valid science
whatever. Those who have the third view regard the
entire history of human knowledge from its beginnings
with primitive man to the present as best understood
when we regard it as a progressive discovery of reality
through forms of knowledge which are never final.
From this third point of view no new theory, however
revolutionary, is judged a priori to be impossible. It
must have its opportunity to show, if it can, that it

viii

INTRODUCTION

accounts for all facts old and new better than the theo-
ries which it would replace. But the more revolutionary
the new theory the more difficult its task.

The Indiana University gladly welcomes scholarly
debate upon the facts and issues involved in the Theory
of Relativity.

William Lowe Bryan

THE FOUNDATION PRINCIPLES OF
RELATIVITY

The Opening Arguments of the Affirmative by Pro-
fessor R. D. Carmichael.

Upon receiving the invitation to speak on this oc-
casion I expressed an unwillingness to engage in de-
bate on relativity in the spirit of seeking a victory over
my opponents, but said that I would enjoy a debate
in the spirit of a search for the truth. I added a
statement of my assurance that the latter was intended,
since such a chapter of Sigma Xi as I know that at In-
diana to be would sponsor no debate except that which
has the search for and exhibition of the truth as its
guiding purpose. This occasion is one of great pleasure
to me in that it allows me to renew my association with
that chapter of Sigma Xi which did me the honor of
electing me into this excellent society. I return to you
with joy as to my Alma Mater in Sigma Xi just as I
returned here last year with joy to my Alma Mater in
Phi Beta Kappa to deliver the annual oration. This
double memory of me by my friends in Indiana Uni-
versity, and these so closely connected invitations to
appear before you in two so widely separated fields,
are very gratifying to me ; and I want here and now to
express my appreciation of them.

On the matter of relativity I have definite con-
victions, but I hold them subject to revision in the
presence of new discoveries or unexpected logical

2

A DEBATE ON RELATIVITY

difficulties in the theory itself. I held these convictions
(or at least some of them) at a time when many people
ridiculed the idea of relativity; and I delivered at In-
diana University in 1912 (but not without trepidation)
what appears to have been the first course of lectures
on relativity given on the American continent, having
been inspired to do this by the kindly encouragement
of Professor Rothrock ; and the notes of these lectures
were published in a little book which is now in its
second edition.

During the intervening years I have continued to
believe in the theory and have witnessed with pleasure
its growth and development. I have enjoyed seeing it
gain adherents year by year so that now it no longer
requires courage to uphold the theory. On the con-
trary it requires courage to oppose it. From time to
time I have heard reports of the destruction of the
theory and rumors of such reports. Formerly they
caused me a certain flutter of excitement, but now they
do so no longer. I have seen the theory of relativity
gaining place in spite of all such reports and all rumors
of such reports. Consequently I am not alarmed by
the new and important experiments of D. C. Miller
which have so renewed the hearts of the opponents of
the theory ; but I expect them, when the actual findings
are determined with accuracy, to take their place in the
theory of relativity or in a modified form of it.

The evidence how appears to me to be conclusive
that the theory of relativity has come to stay, not with-
out development and improvement to be sure, but with-
out such change as will destroy its essential character.
It may be included in a later and more comprehensive

FOUNDATION PRINCIPLES OF RELATIVITY

3

theory in the same way as that in which it has included
its predecessors, but thinkers will never return to the
old way of thinking in vogue before the appearance of
relativity.

If I am wrong in this conviction and confidence, I
count myself fortunate now to be in a position to re-
ceive my due punishment for such error ; for I believe
with Socrates, as reported by Plato, that the due pun-
ishment of a man for error is to be set right by those
who know. Therefore in undertaking to uphold my
conviction and to transfer to you my confidence in the
theory of relativity, I count myself doubly fortunate
to meet two such speakers and thinkers as the local
chapter of Sigma Xi has opposed to me in this friendly
encounter — an encounter, I believe, whose spirit is that
of search for the truth, unmarred by the desire for
personal victory.

At the opening of this debate I am reminded of a
happening at the time of the last preceding great ad-
vance in scientific thought, comparable to relativity
both in importance and in the stir of public interest and
curiosity which it excited. I refer to the famous Hux-
ley-Wilberforce debate on Darwin’s theory of evolu-
tion. In that great encounter the Bishop, primed with
“facts” misunderstood, came forth

“To meet, for the first time in all his life,

Stark earnest thought, wrestling for truth alone,
As men on earth discerned it”
and seemed to many of his auditors to win clear vic-
tory ; but according to the verdict of history, he suffered
ignominious defeat. As for his opponents (I quote
Alfred Noyes),

4

A DEBATE ON RELATIVITY

“They trusted in the truth. They could not see
Where it might lead them. Only at times they felt
As they deciphered the dark Book of Earth
That, following its majestic rhythm of law,

They followed the true path, the eternal way
Of that which reigned.”

After the tumultuous applause which followed the
Bishop’s well rounded oration

“The lean tall figure of Huxley quietly arose.

He looked for a moment thoughtfully at the
crowd ,

Saw rows of hostile faces ; caught the grin
Of ignorant curiosity : here and there,

A hopeful gleam of friendship; and, far back,
The young, swift-footed, waiting for the fire
[Of truth to carry on the conquering Torch].

He fixed his eyes on these — then, in low tones,
Clear, cool, incisive, ‘I have come here,’ he said,
‘In the cause of science only.’ ”

In this debate we are fortunate in the fact that both
sides have come here in the cause of truth alone ; and
in the spirit actuated by such a cause we shall carry on
our discussions. Though relativity is new the time has
come for it to win; and I am here tonight to add a
little bit of impulse to hasten the day of its final tri-
umph.

But the problem of relativity is far too serious a
matter to be settled by such a debate as this. A full
analysis of the subject requires the technical machinery
of a complicated and advanced mathematics ; and this
is clearly out of the question on the present occasion.
We Can hot here settle the argument ; we can only hope

FOUNDATION PRINCIPLES OF RELATIVITY

5

to advance it in the minds of some of you.

No sort of mechanics can be developed without
some kind of principle of relativity. There is a cer-
tain sort of relativity of space involved already in the
old geometry of Euclid, as Birkhoff has so happily
emphasized in his recent book on “The Origin, Nature,
and Influence of Relativity ■" This is modified in the
more restricted relativity involved in the Galileo-New-
tonian mechanics ; and the latter theory of relativity —
without being called by this name — has flourished for
several generations in the classical theoretical physics.
A new and more comprehensive relativity was intro-
duced by Einstein in his restricted theory as presented
in 1905. The most significant extension of this was
made by Einstein himself in his memoir of 1916; and
this theory has been developed and extended and modi-
fied by others since then, notably by Weyl and Edding-
ton and Whitehead.

It becomes, then, a question, not of having or not
having a theory of relativity, but of what theory of
relativity one shall hold. The name Theory of Rela-
tivity, by a sort of historical accident, has become at-
tached to that sort which has been developed by Ein-
stein and his followers. We may call it “the Relativity
belonging to die Einstein tradition”. In opposing this
theory of relativity, our opponents, it is to be presumed,
will tell us what theory they profess and will under-
take to remove the difficulties which we may show it
to possess.

For our part we shall support the relativity be-
longing to the Einstein tradition.

Such relativity will be modified and extended and

6

A DEBATE ON RELATIVITY

developed, but we will never go back to the older ways
of thinking. What has been achieved is not perfect ; it
is not ultimate. There is nowhere a scientific theory
which is perfect and ultimate. But the theory of rela-
tivity comes nearer to this ideal than any of its rivals.
The cause of the older physics, in so far as it is op-
posed to relativity, appears to me to be already a lost
cause, even though there are still those who are ready
to support it. Its advocates are evidently alive though
the cause itself seems to be lost. And a cause once lost
nearly always remains a lost cause.

Before we proceed to an analysis of the basis of
the general theory of relativity we must give attention
to still a few other preliminary considerations.

It is necessary to draw a careful distinction be-
tween the laws and the principles of physical science.
The two things are different though they have not al-
ways been sharply distinguished. It is very important to
us now to draw the distinction ; and it is convenient to
use these two words to express the difference in thought.

By a law we shall mean a statement of phenomenal
fact in terms involving numerical relations subject to
experimental verification by measurement. By a prin-
ciple we shall mean a statement of fact, relating to
phenomena, in such a form as to require a transforma-
tion by the use of other facts before one can arrive at
1 numerical relations subject to experimental verifica-
tion by measurement.

With this use of terms we should speak, for in-
stance, as is customarily done, of the Principle (rather
than the Law) of the Conservation of Energy. But
we shall speak of Newton’s Law of Gravitation. The

FOUNDATION PRINCIPLES OF RELATIVITY

7

former expresses a general principle which must be
transformed by means of other facts before one can
arrive at numerical relations subject to experimental
confirmation by measurement; the latter states a phe-
nomenal fact (in so far as it is true) in terms of a
numerical relation subject to experimental confirma-
tion by measurement. Following this terminology, we
should speak of the Principle of Evolution and Men-
del’s Law of inheritance.

Both laws and principles have been of fundamental
importance in the development of physical science. We
can not dispense with either of them. But the prin-
ciples of physical science are not subject to a direct
proof or disproof. This is true of the Principle of the
Conservation of Energy. There is no direct proof of
it; and in the nature of things it is difficult to see how
there could be. And yet it is of so fundamental a char-
acter that without it the structure of modern physical
science would collapse. It may be modified ; it may be
combined with the Principle of the Conservation of
Matter into a new form which embraces the two older
principles. But we can not dispense with it without
building up the whole of our science on some new
basis not yet known to us. The value of the principle
is in the guidance which it affords both to experiment
and to a logical organization and coordination of physi-
cal science. Many of the results attained or explained
by aid of it, in conjunction with other facts, are sub-
ject to experimental verification; but the principle itself
is not subject to direct test. Its value and presumptive
accuracy are determined by an analysis and examina-
tion of the results obtained by means of it.

8

A DEBATE ON RELATIVITY

No one disputes the value of what has been a-
chieved by means of the principle of the conservation
of energy; and therefore no one can properly object to
a principle on account of the fact that it plays a role
similar in the respects indicated to that of the principle
of the conservation of energy.

Now one main part of the basis of the theory of
relativity rests, as we shall see, in certain principles
which underlie the development of the theory. When
we come to them it will be well to remember the role of
a principle as exhibited by the examples just given.

It is important to have clearly in mind the rela-
tion of relativity to the facts of physical phenomena
before we proceed to the analysis which is to result in
the principles of relativity.

There is no experimental fact, tested and corrob-
orated, which is clearly known to be in contradiction
with relativity. There are facts, of course, which have
not been brought under its domain. This is fortunate,
since a comprehensive synthesis might represent a dead
end, leading to no further progress for a long time; but
the quantum theory has appeared with a new set of
facts partially outside the scope of the present rela-
tivity physics ; and these new facts beckon us to fur-
ther discoveries not yet made. There are facts, then,
which have not been brought under the domain of rela-
tivity; there are some which have been erroneously
thought to be in contradiction with it; and there are
some about which we do not know what to say at pres-
ent for lack of sufficient evidence or of a sufficient
analysis. If the debaters here can present any facts
which they think to be in contradiction with the theory

FOUNDATION PRINCIPLES OF RELATIVITY

9

of relativity we will do one of four things, so far as
time will permit; we will undertake to show that the
charge of contradiction is not convincingly supported,
or we will repel the charge with convincing evidence,
or we will show that the facts alleged do not come
within the domain of the present relativity physics, or
we will acknowledge either the validity of the charge
or of our inability to refute it. Unless some fact or
facts at present unknown to us are given we will re-
fute the charge of established contradiction. We admit
the possible existence of conclusions about which we
can not say with certainty whether they contradict or
support the theory of relativity, because nobody knows
with certainty. Obviously we can not marshal all facts
and show their agreement with relativity ; but we are
prepared to examine all facts presented and to deal
with them as we have already said.

We believe furthermore that no such comprehensive
agreement with phenomena can be claimed for any ri-
val theory.

In this connection it is important to remember that
most observed phenomena are in agreement both with
relativity and with the classical theory, the two doc-
trines giving rise to conclusions which are so nearly
identical, so far as observational confirmation is con-
cerned, that the numerical differences are within the
limits of experimental error.

' My colleague will tell you about the remarkable
\ I conquests of the theory of relativity in connection with
i^the three so-called crucial experiments suggested by
| Einstein. I may anticipate his analysis to the extent
| of saying in a preliminary way that the theory has ex-

10

A DEBATE ON RELATIVITY

plained the long-standing anomaly in connection with
the perihelion advance of Mercury, that it has predicted
the bending of a light ray in the neighborhood of the
sun and that this prediction has been verified, and that
it has predicted the shifting of spectral lines in light
coming from the sun or other large bodies and that this
prediction has been verified by observation not only of
light from the sun but also of that from the White
Dwarf, the illustrious companion of Sirius. You see
that the theory has been verified by crucial phenomena
arising in the solar system and by phenomena from
regions beyond the confines of the solar system.

Thus Einstein has given us signs in the heavens to
corroborate his theory and mankind will never go back
on signs in the heavens. A theory so supported by
celestial witnesses is one which has come to stay.

In a letter to a London paper a few years ago Ein-
stein said that if relativity should prevail then in Ger-
many he would be a German scientist while in England
he would be a German Jew, whereas if the theory
should fail to be confirmed then in England he would
be a German scientist while in Germany he would be a
German Jew. If this relativistic proposition is true,
then the Germans will call Einstein a German scientist
while the English will call him a German Jew.

What is the origin, what is the nature, and what is
the import of a system of thought which conquers on
the earth and in the silent depths of distant space? To
answer this question is our present task.

The position of a ship at sea may be defined by giv-
ing two numbers, its latitude and its longitude; it is a
two-dimensional matter. To define the position of an

FOUNDATION PRINCIPLES OF RELATIVITY 11

aeroplane at sea requires latitude and longitude and
height above sea-level ; it is a matter of three dimen-
sions. In both of these cases we have spoken of po-
sitions merely. The primary things of physical science
are not positions hut events, things which happen.
Now nothing ever happened in a portion of space
without happening also in an interval of time. To lo-
cate an event we have to specify four numbers; it is
a matter of four dimensions. In the usual language
three of these are said to belong to space and one to be-
long to time. According to the theory of relativity
the space and the time of an event are not two inde-
pendent things. This is the primary innovation of
Einstein. To assume that they are independent, as
was universally done before the advent of the theory
of relativity, is to introduce into our interpretation of
phenomena an element of hypothesis which is not sup-
plied by the facts. On this hypothesis we can build a
mechanics which has a certain very close approxima-
tion to the facts as we know them. But if we want a
thoroughly adequate account of phenomena we must
proceed to more fundamental considerations and we
must deny ourselves the apparent convenience of the
hypothesis of a fundamental sepaiation of space and
time.

It is desirable to dwell a little longer on the fact that
the fundamental things in physical science are events.
There is no such thing as an atom at an instant of time.
It requires a certain interval of time for an atom to be
an atom. A manifestation of activity is one of the
things necessary to its existence as we conceive it, and
activity can not be manifested at an instant ; a certain

12

A DEBATE ON RELATIVITY

duration of time is necessary to the exhibition of its
properties and hence to its existence as we know it.
Moreover, a certain portion of space, and not a mere
point, is necessary as the scene of its activities. It is
m connection with these facts, more than any other,
that the Einstein synthesis falls short of the ultimate.
It uses a special model of interstellar space, empty ex-
cept for point particles, and it conceives time as made
up of instants. This is a conception of things which
is not true to facts and it can hardly be supposed that
any theory is ultimate which begins from a conception,
or a model, of things not in entire accord with phe-
nomena. There is then, apparently, something yet
necessary to bring the Einstein synthesis to the highest
conceivable perfection. Whitehead has made an im-
portant contribution in this direction, but there still
remains much to be done. While the Einstein theory
has moved in the right direction it has not yet reached
the goal of the ultimate.

Let us linger a little longer over one element in the
notion of an event in order to emphasize the fact that
events are not matters in which space and time are
separated. An event takes place where it occurs and
when it occurs, and the where and the when are not
separated in experience but are in the most intimate
union and conjunction. It is only in thought that we
have separated them. For a time this separation in
thought was useful and convenient to us, but it has
lately led us into difficulties. What more natural thing,
then, could be done than to agree to dispense with a
convention wljich has served its purpose and has finally
betome uncomfortable to us? In the theory of rela-

FOUNDATION PRINCIPLES OF RELATIVITY 13

tivity we propose to do away with this convention and
to allow space and time to be commingled in our
thought as they always have been in our experience.
Henceforth, m thought as well as in experience, space
by itself and time by itself, as Minkowski has said,
are to be mere shadows and only a union of the two
shall be conceived as having real existence.

Let us enquire how this radical return of thought
to the basis of experience has come about.

If a swimmer can go a certain distance d miles in
still water and return in t seconds, his velocity being c
miles per second, then in a stream flowing with a veloc-
ity of v miles per second he can swim directly across a
distance d and return in st seconds where

s^l/yJl—v-Zc* ,

and he can swim a distance d upstream and back in
s 2 t seconds. These two times differ by a measurable
amount. If the times were determined by experiment
and the velocity of the swimmer in still water were
known, one could compute the velocity of the stream.

The principle involved in this simple example un-
derlies the experiment from a consideration of which
the theory of relativity took its rise. If the earth is
moving through the ether of space (supposed existent
at the time the experiment was made) this fact should
affect the phenomena of light and of electromagnetism.
In particular, a light ray should make its journey
across the ether stream to a mirror and back in less
time than would be required if the same journey were
made along the ether stream and back. But the early
experiments of Michelson and Morley showed no such

14

A DEBATE ON RELATIVITY

difference in time. These experimenters failed to
detect a motion through the ether. (On account of
the recent work of D. C. Miller a further analysis must
now be made of the Michelson and Morley experiment :
this we shall give you tomorrow night.) Several other
experiments were made in the attempt to detect mo-
tion through the hypothetical ether, and all of them
showed a negative result. It was impossible to detect
any effect whatever of the supposed ether upon the
facts of experiment, though trials of various sorts were
made. Even in the light of the recent experiments
of D C. Miller, as we shall show more fully tomorrow
night by an examination of that experiment and several
others, the preponderating evidence is still in favor of
the conclusion that motion through a hypothetical ether
can not be detected by observation of phenomena on
the moving system. There is too great a convergence
of evidence from several sources for us seriously to
question the conclusion on the basis of a single experi-
ment the implications of which are not yet fully under-
stood, eve'n though that experiment is acknowledged
to be one of fundamental importance.

Now no one has ever succeeded in assigning to this
hypothetical ether a set of consistent properties which
will bring the hypothesis of its existence into agree-
ment with all the relevant facts. This does not mean
that no one will ever do so; but it does justify us in
formulating our laws and principles of nature in a form
to be independent of the ether, if we are able to do so ;
and in the theory of relativity a reasonable success in
this direction has been made. Let us then, for the pres-
ent, formulate some of the conclusions of experimental

FOUNDATION PRINCIPLES OF RELATIVITY 15

fact without employing any conception of the ether.
We will do this in general terms for the sake of brevity.
In the first analysis we shall suppose that the gravi-
tational field is sufficiently small to be treated as neg-
ligible.

In order to be able to deal with such quantities as
are involved in the measurement of motion, time, ve-
locity, etc., or, indeed, in the quantitative analysis of
any physical phenomena, it is necessary to have some
system or systems of reference with respect to which
measurements can be made. Let us consider any set
of things consisting of objects and any kind of physical
quantities whatever, as electric charges or magnets
or light-sources or telescopes or other objects and in-
struments, each of which is at rest with respect to each
of the others. Let us suppose that among these objects
are clocks, to be used for measuring time, and rods or
rules to be used for measuring lengths, and that time
and length may be measured at any desired instant and
any assigned place. Such a set of objects and quanti-
ties and instruments, including the equipment for meas-
uring time and length, all being at rest relatively to
each other, we shall call a system of reference. Such a
system we shall denote variously by S', S 7 , S lt S 2 , etc.

In order to formulate some of the principles we
need also the conception of free space. Free space is)
a portion of space in which no gravitational or electro-
magnetic or other field is present. In practice we shall
use for free space any portion of space in which such
fields are so weak as to be negligible.

The Restricted Principle of Relativity may now be
stated in the following form ■ If and S 2 are two sys -

16

A debate on relativity

terns of reference in free space having with respect to
each other a uniform unaccelerated motion, then natur-
al phenomena run their course with respect to S 2 in
accordance with precisely the same general lazvs as with
respect to S x .

This principle says nothing about the suitability of
any particular system of reference for the convenient
expression of the laws of nature; but it does say that
if either S 1 or S 2 is suitable the other is equally suitable,
when the conditions named are satisfied.

In order to bring into convenient relations the
measurements made on two systems of reference it is
necessary to have some agreement concerning the cor-
respondence of units. Accordingly, we shall make use
of the following Principle of Correspondence of Units.
The units of any two systems and S z are such that
the same numerical result will be obtained on measur-
ing with the units of a quantity L x and with the units
i’a a quantity L 2 when the relation of L t to is just
the same as that of L 2 to

Let us suppose that the restricted principle of rela-
tivity is to be understood in a sense which implies this
agreement concerning the correspondence of units. As
so interpreted we believe that the restricted principle
of relativity is in agreement with the facts of experi-
ment and observation.

There are two characteristic postulates or laws of
nature implied by the restricted principle of relativity.
They may be stated as follows :

The unaccelerated motion of a system of reference
5 in free space can not be detected by observations
made on S alone, the units of measurement being those

FOUNDATION PRINCIPLES OP RELATIVITY 17

belonging to S.

The velocity of light in free space, when measured
on an unaccelerated system of reference 6" by means of
units belonging to S, is independent of the velocity of S'
and of the unaccelerated velocity of the light source.

There are three other postulates or laws which we
now need, and these are common to the restricted
theory of relativity and the Galileo- Newtonian mechan-
ics. They may be stated in the following form:

If two systems of reference Tj and S 2 move with
unaccelerated relative velocity and if a body moves
relatively to one of the systems in a straight line with
unaccelerated velocity then it also moves in a straight
line relatively to the other and with unaccelerated ve-
locity.

If the velocity of a system of reference S 2 relative
to a system of reference S x is measured by means of
units belonging to S 1 and if the velocity of S t relative to
S 2 is measured by means of units belonging to S 2 the
two results will agree in numerical value.

If two systems of reference and S„ move with
unaccelerated relative velocity and if a line segment l
is perpendicular to the line of motion of S x and S 2 and
is fixed to one of these systems, then the length of /
measured by means of the units belonging to ^ will be
the same as its length measured by means of the units
belonging to S 2 .

It should be observed that the last three postulates
are merely explicit statements of principles which un-
derlie the classical Galileo- Newtonian mechanics ; they
are common to that theory and the restricted theory
of relativity. Since the latter may be derived in toto

18

A DEBATE ON RELATIVITY

by means of these postulates and the restricted prin-
ciple of relativity, together with the characteristic laws
implied by it, it follows that all adherents of the Gali-
leo-Newtonian mechanics must find in the restricted
principle of relativity alone the ground for their ob-
jections to the theory. We may therefore expect this
principle to play an important role in our further dis-
cussions.

From these postulates one may readily derive the
formulas for the celebrated Lorentz transformation
of space and time coordinates, Let two systems of ref-
erence F and S' have the relative velocity v in the line
l. Let systems of rectangular coordinates be attached
to the systems of reference F and S' in such a way that
the .Y-axis of each system is in the line l and that the
two axes have the same positive direction ; and let the
y-axis and the 2-axis of one system be parallel to the
y-axts and the s-axis respectively of the other system
and have their positive senses in the same directions.
Let these two axes coincide at the time zero. Further-
more, for the sake of distinction, denote the space and
time coordinates on S' by x, y, s, t, and those on S' by
x\ y', s', t'. Let us suppose that S' moves with respect
to S in the direction of increasing values of x in the
system on S. Then it may be shown, on the basis of
the named postulates, that the values of t', x\ y', s' in
terms of t, x, y, s are expressed by the formulas,

fle'=s-

1 / 1 -/ 3 2
1

vT=i

FOUNDATION PRINCIPLES OF RELATIVITY 19

y'=y,

= 2 ,

where /?— v/c and c is the velocity of light. These
formulas define the Lorentz transformation.

It is important to remember that the Lorentz trans-
formation already had a fundamental place in physical
science before the advent of the theory of relativity,
but it was not grounded in a general principle of fun-
damental importance as it is in relativity. It is the
great glory of Einstein that he saw how to ground it
in a general principle and later to proceed from it to his
fundamental theory of gravitation.

It is not difficult to show that all the essential parts
of the restricted theory of relativity are bound up in
these equations and the interpretation of them which is
implicit in the method by which they are derived. It
is therefore important to our present purpose to put a
part of their meaning into common every day language,
such as may be understood by those who are repelled
by the mathematical formulas.

The first truth that we shall associate with them is
one which was discovered by Einstein: There is no
such thing as the absolute simultaneity of events hap-
pening at different places.

It is important to get a clear grasp of the implica-
tions of this statement, What shall we mean by saying
that two events which happen at different places are
simultaneous? First of all let us notice that we have
no direct sense of what such simultaneity should mean.
Two experiences which I myself have may be called
simultaneous if they are so interlocked that I can not
separate them without mutilating them. But if two

20

A DEBATE ON RELATIVITY

things happen which are far removed from each other
I do not have a direct perception of them in such a way
as to perceive them as simultaneous. When should I
consider such events to be simultaneous ?

If you examine this question with a clear analysis
you will see that you can not give any absolute answer.
It is necessary to invent some technical means of de-
fining such simultaneity. The definition will depend
upon the system of reference from which measurements
are being made; and it will be different for two ob-
servers upon systems which are not at rest relatively
to each other. There is therefore a certain element of
convention or agreement in every such definition. There
is no such thing as absolute simultaneity of events
which are separated in space ; simultaneity is a relative
matter.

It is, however, not an arbitrary matter. While it
is not defined by any absolute means it is yet restricted
within certain limits. Let us make clear the nature of
this restriction. In this analysis we need to make use
, of the fact that the velocity of light is the greatest ve-
l locity which exists in the physical world. No object
or disturbance has ever been known to move faster
than light. There is an inherent impossibility in the
well known limerick:

“There was a woman named Wright
Who moved about faster than light.

She went out one day
In a relative way

And returned the preceding night.”

Now consider a particular event, as the running of
this watch, for instance. Let us use the phrase, the

FOUNDATION PRINCIPLES OF RELATIVITY 21

active past of this event, to denote those happenings in
time which are close enough, relatively to their position
in space, to have a possible chance of affecting this
event. In the four-dimensional world of space and
time this will be a cone stretching backward in time
from the running watch which is at its vertex. Every
happening in this cone — and no other — will be said to
belong to the active past of this event afforded by the
running watch. A happening five hundred years ago
on a star a thousand light-years away is too recent to be
in the active past of this present event here, since no
influence from it has yet had time to reach this event.
Moreover, nothing within the next thousand years can
happen here so as to affect the star which is a thousand
light-years away, since no influence arising here and
now will reach it in less than a thousand years. Thus
we are led also to the conception of the active future
of this present event. This active future consists of
all the happenings which are close enough in time, rela-
tively to their position in space, to have a possible
chance of being affected by this present event. This
active future is a cone in the four-dimensional world
of space and time which stretches forward in time from
this present event which is at its vertex.

Thus the active past of this event is a four-dimen-
sional cone stretching backward in space and time;
while its active future is a similar cone stretching
forward in space and time. Any part of the four-
dimensional world which is outside of both of these
cones is neither in the active past nor in the active fu-
ture of this present event. All such parts of the four-
dimensional world may be said to be contemporaneous

22

A DEBATE ON RELATIVITY

with this present event. Thus physical time has a sort
of conical order, as Robb has called it, and not a linear
order. It is due to this fact that simultaneity can not
be an absolute matter while it is also not an arbitrary
matter. By any proper definition of the simultaneity of
two events, neither must be in the active past or in the
active future of the other. Each must be in the region
of contemporaneousness with the other. Within the
limits thus set simultaneity may be defined in any con-
venient way. We can not now go into the technical
means by which simultaneity may be conveniently de-
fined on a particular system of reference, inasmuch as
that is not necessary to the analysis of the principles
of relativity as we are now developing them.

Let us point out some other consequences of the
Lorentz transformation and hence of the restricted
theory of relativity. To an observer A on one system
the clocks on another system in relative motion with
his own will appear to run more slowly than his own,
while to an observer B on the second system the clocks
of the first system will appear to run more slowly than
his own. To each the unit of time of the other appears
to be greater than his own. Again, to each of them it
appears that the unit of length of the other, in their
line of relative motion, is longer than his own. These
differences are inherent in the nature of things and
can not be effectively removed' by any conventional
agreement. Addition of velocities follows a new law.
The velocity of light is a maximum velocity in nature.
The mass of a body increases as its velocity is increased,
so that there is a tendency to treat mass and energy as
essentially interchangeable. But, above all, space and

FOUNDATION PRINCIPLES OF RELATIVITY 23

time are entangled and commingled so as to be quite
inseparable. Thus theory has kept together the space
and the time which have always been commingled in
our experience.

After the severe shaking up due to the restricted
theory of relativity and the experiments out of which
it grew, theoretical physics was ready to start over
again and to make further progress with the problems
of space and time and motion — the most important and
the most fruitful problems with which physics has had
to deal. The essential step of progress was made by
Einstein with his general theory of relativity announced
in his memoir of 1916.

Now if space and time are conjoined or entangled
in experience so 'that we can no longer profitably sepa-
rate them in thought, we are not justified in dealing
with a space of three dimensions separated from the one
time dimension, but we must deal at once with the one
thing which we may call space-time — not space and
time, not the addition of two things, but one thing, a
thing for which we have no word, since it is a new
conception. We call it space-time for lack of a bettei
term.

This four-dimensional manifold of space-time is the
fundamental starting point of the general theory of
relativity. In physical science it is essential that we
say both where and when a thing is or an event occurs
— and these are not two things but one. They can be
separated only by a convention that has an element of
arbitrariness in it. It is due to the inadequacy of lan-
guage that we have to speak as if we referred to parts
conjoined. Having no words for the whole we have

24

A DEBATE ON RELATIVITY

to refer to the artificial parts which language names.
But, nevertheless, let us hold clearly to the fact that to
call for where and when is to call for one thing, name-
ly, the space-time location of an event.

Keeping these considerations in mind let us lead
up to and present the basic principles on which Einstein
founded his general theory of relativity.

In the first place we must keep clearly in mind a
fact which has sometimes been lost from view. The
restricted theory of relativity was not discarded in
formulating the general theory; on the contrary, the
former was wrought intimately into the structure of
the latter. In the process it became evident that the
restricted theory was subject to some limitations not
at first fully realized — limitations as to the circum-
stances of its validity. But with these limitations,
which we have wrought into the foregoing formulation,
this theory has been incorporated into the general
theory. This has been done in two definite and specific
ways, as we shall now make clear.

In the general theory it is still maintained that the
restricted principle of relativity shall hold, subject to
the stated condition that the phenomena involved occur
in free space. This affords a sort of limiting condition
by means of which certain properties of the gravita-
tional potential may be established. There is no con-
dition in nature in which this principle can be applied
with strictness just as there is no condition when un-
disturbed motion in a straight line can be realized in
the Newtonian mechanics. But it is an ideal condition
which reflects itself in limitations on the form of the
gravitational potential ; in this way it comes to be sub-

FOUNDATION PRINCIPLES OF RELATIVITY 25

ject to indirect experimental test. The maintenance of
the restricted principle of relativity in free space serves
to afford limiting conditions or boundary conditions at
infinity, so to speak ; and these are essential to the de-
velopment of the general theory.

In connection with Newton’s law of gravitation you
have all heard the story of the falling apple. Since
Einstein has given us a law of gravitation to replace
that of Newton it is fitting that a like story of a fall-
ing object should be associated with him. I do not
vouch for its historical accuracy, but it affords a con-
venient means of introducing an important principle.

The story is told that Einstein was watching a la-
borer on a high scaffold engaged with others in the
construction of a building and that he saw the laborer
lose his balance and fall to the ground. Fortunately
the laborer was not seriously hurt. On seeing this, so
the story goes, Einstein ran up to the laborer in greaf
excitement, and the following colloquy took place:

“My dear sir, did you feel anything pulling on you
as you came down?”

“What?”

“Did you feel anything pulling on you as you came
down ?”

“No, I just fell.”

The laborer could not see that he needed to have
anything pull on him to make him come down. He just
fell.

Let us idealize this story into a sort of mental ex-
periment. Let us suppose that an observer is inclosed
in a sealed laboratory so that he can observe nothing
except what is taking place in his laboratory. Suppose

26

A DEBATE ON RELATIVITY

that the laboratory is unsupported by other bodies
and that it is falling freely in space without rotation.
If in such a laboratory an obiect is placed at a
given point in the open air it will remain fixed there.
If it is given a motion in any direction whatever rela-
tive to the walls of the laboratory it will continue in
motion in a straight line relative to the walls of the
laboratory until it is impeded by some resisting force.
An observer in such a laboratory would find himself,
to all intents and purposes, in a state of freedom from
any gravitational field whatever. Weight has dis-
appeared. If one leaps upward with ever so little
force he will go to the top of the laboratory. If he
takes his place in the middle, not touching either top
or bottom or walls, he will remain stationary there.
The gravitational field is non-existent for him. The
relativity of the situation is incomplete, however, as
would be shown by the behavior of a magnetic needle.

Now what does this absence of a gravitational field
signify ? Within this laboratory phenomena (events)
run their course independently of gravitation, provided
that they are considered only in their relation to the
laboratory itself and to one another in the laboratory.

But now suppose that the laboratory is falling
toward the earth and is being observed from a station
on the earth. It is found that it is falling with a con-
stantly increasing velocity; that is, it is subject to an
acceleration — just the acceleration which is due to the
gravitational field through which the laboratory is mov-
ing. It is this acceleration which has balanced, or dis-
pensed with, the gravitational field. We may say that,
so far as the laboratory is concerned, the acceleration

FOUNDATION PRINCIPLES Or RELATIVITY 27

field is equivalent to the gravitational field and is op-
positely directed so that the two fields balance each
other.

Now suppose that some upwaid pull decreases the
acceleration of the laboratory relative to the earth with-
out overcoming it entirely. A part of the gravitational
field will still be overcome, but another part will re-
main and manifest itself as a reduced gravitational
field in the laboratory.

Let us now reverse the pull on the laboratory and
bring it down with a greater acceleration than that
due to the gravitational field of force. What will then
happen to the objects within the laboratory? They will
all fall to the top of the laboratory and will remain
stationary there ; and it will require force to lift them
from the top just as it ordinarily requires force to lift
objects from the bottom of our laboratories sta-
tioned on the earth. This means that the gravitational
force is not only balanced out in the laboratory but that
it is actually reversed in direction. We have intro-
duced an acceleration field which is too strong for the
gravitational field and has effectively reversed it in
direction so that we have a gravitational field upward
instead of downward.

What I want you to see from this is the following :
By the introduction of an appropriate acceleration we
can modify or annihilate or even reverse the gravita-
tional field of force in the moving laboratory. By an
appropriate pull of the laboratory to one side we could
also produce a sidewise gravitational field.

Now if an acceleration field can so modify locally
a gravitational field and even reverse it, there must be

28

A DEBATE ON RELATIVITY

some sort of fundamental equivalence between the two.
This general conclusion may be formulated more pre-
cisly as one of the important foundation principles of
the general theory of relativity. It means that we
should choose as our fundamental four-dimensional
geometry one in which we should no longer find it
necessary to postulate forces to account for motions
in a given sufficiently small portion of space.

We shall attempt a precise formulation of this Prin-
ciple of Equivalence in the following words;

For a sufficiently small region of the four-dimen-
sional world of space-time, that is, a region so small
that the variation of gravitation in it in both time and
space is negligible, there exists a coordinate system,
or system of reference, with respect to which gravi-
tation has no appreciable influence either upon the
motion of mass particles or upon any other physical
phenomena whatever.

As a commentary we may add the remark that if
there is no electro-magnetic or other field present it is
to be understood that the restricted theory of relativity
is valid in this small portion of space-time, since it is
then effectively a small portion of free space. This
is the assumption made by Einstein and it is abundantly
justified by the fact that the restricted theory is in
such close agreement with so many phenomena of
observation and experiment. It is not a speculative
hypothesis but one that seems to be demanded by the
facts of nature.

Thus we see that there are two ways in which the
restricted theory of relativity is incorporated intimately
into the general theory. To put it roughly, they are

FOUNDATION PRINCIPLES OF RELATIVITY 29

the following: In the absence of a gravitational field
and of electromagnetic or other disturbance, the re-
stricted theory of relativity is to hold; in sufficiently
small portions of space-time it is valid within the range
of a vanishing difference due to macrocosmic phenom-
ena.

There is still one other general principle upon which
Einsetein has insisted, namely, the so-called Principle of
Covariance. The following considerations will en-
able us to arrive at its meaning.

When a mathematician or a theoretical physicist
wishes to speak in detail about physical phenomena,
and especially the phenomena of motion, he introduces
a system of coordinates x, y, z, t by means of which
to define the positions of particles at the various in-
stants of time. Now there are no such coordinates in
nature. No one ever saw these quantities x, y, z, t
either stationary or moving around among phenomena.
They have been inserted by the thinker into the picture
from which they are absent in nature. There is no
objection to having this done, since it serves a great
purpose of convenience. But proper allowance must
be made for the fact that these coordinates x, y, z, t
have been inserted into phenomena in which they have
no place as a fact of the actual occurrences. They
serve a useful purpose as a scaffolding to help sustain
the thought during the process of investigation and
discovery. But in the ultimate picture to be retained
by science they can have no place since they are absent
from nature. When the structure of science is com-
pleted this scaffolding should be torn away. It should
not remain as a part of the ultimate explanation of

30

A DEBATE ON RELATIVITY

phenomena. These coordinates, having been intro-
duced by thought as a matter of convenience, must be
taken out of the picture formed by thought before
that picture can be considered complete.

In more precise, but still non-technical language:
The laws of nature should be so expressed in terms of
the coordinates employed as to be essentially inde-
pendent of the coordinates chosen so that if we used
some other system of coordinates these laws should
have in them the same expression as in those actually
employed

The extreme naturalness of this requirement must
be apparent to everyone, since elements not involved
in phenomena should not form an essential part of the
explanation of them. It is so simple in its general for-
mulation that we may dispense with an exact mathe-
matical statement.

We have now before us the three fundamental re-
quirements of the general theory of relativity so far
as gravitational fields are concerned. We shall not
undertake to go into the extensions which have been
proposed for dealing with electromagnetic phenomena,
even though the latter are important, for all the essen-
tial questions concerning the validity of the relativistic
point of view are, I believe, fully apparent in the theory
of gravitation. By confining attention to this we will
center our thought and make more effective progress
toward understanding the theory.

Whether the laws of nature, as manifested in the
results of experiment and observation, can be subject
to these three fundamental requirements is the prime
question to be answered in the general theory of rela-

FOUNDATION PRINCIPLES OF RELATIVITY 31

tivity as it stands today. It is a question which can not
be answered apart from experiment itself. To settle it
requires much careful consideration. And the answer,
as given up to the present, is an incomplete one, as is
evidenced by the fact that people are interested in such
a debate as this one. But, so far as present knowledge
goes, it appears to me, as to many others, that the an-
swer must be affirmative. My colleague will show you
tomorrow night in how far the question has been actu-
ally answered in the affirmative by obseivation and
experiment.

For my own part I must now say still a little more
about the general principles underlying the theory, es-
pecially since the application of one of them has some-
times been misunderstood in such a way as to lead to
a wrong conclusion.

According to the principle of equivalence it is pos-
sible so to choose the system of reference, in a limited
portion of space-time, that the restricted theory of
relativity will be valid except for inappreciable devia-
tions from it. Now any other system of reference can
be obtained from such a one by a transformation of
coordinates. In such a transformation the space-time
separation of two near events must be unchanged, for
it is a quantity which is entirely independent of the
system of coordinates. Let us denote this space-time
separation of two near events by ds. Then in the re-
stricted theory of relativity we have

ds 2 — dx 2 -\-dy 2 -\-dz 2 — c 2 dt 2

where c is the speed of light, provided that we employ
units which are both customary and convenient— a re-
lation for which there is much experimental confirma-

32

A DEBATE ON RELATIVITY

tion. Now if we make a general transformation to new
coordinates x x , x 2 , x 3 , x t , the foregoing equation takes
the form

4

ds~= Qij d>Xi dxt j , Q i ji>

y=l

where the g, v j are functions of x X) x 21 x 2 , x v More-
over, it is only an element ds of this form which may be
changed, by transformation of coordinates, to that of
the restricted theory of relativity. Hence the taking
of a quadratic differential form for ds 2 has nothing
arbitrary in it, but is required by the fact that the re-
stricted theory holds in an infinitesimal region of space-
time. This removes at a stroke some of the main ob-
jections which have been raised to taking a quadratic
differential form as the defining form for ds 2 . It is the
only form which makes possible the maintenance of
the principle of equivalence in the light of the fact that
the restricted theory of relativity affords a first ap-
proximation to fact in a small portion of space-time
even if there is a gravitational field,

Granting these three foundational principles of the
general theory and starting from the deep-lying mathe-
matical fact just given, one may build up gradually
and step by step the details of the general theory of
relativity. Unfortunately this can not be done (at
present at least) without the machinery of a technical
and advanced mathematics. From the mathematical
point of view the first thing to be done is to determine
what mathematical relations, involving the previously
namecf coefficients g ih exist in such form as to satisfy
the demand of the principle of covariance. This part

FOUNDATION PRINCIPLES OF RELATIVITY 33

of the work is strictly theoretical, having no further
relations with phenomena except those which have al-
ready been wrought into the expression for ds 2 . It
turns out that there are not many of these mathematical
expressions having a relatively simple form. Conse-
quently all of those of the simpler forms can, be de-
termined.

The question to be considered next is that of their
relation to phenomena. There is no assurance before-
hand that every one of them will correspond to events
in the physical world ; nor is there any a priori means
for deciding which will belong to a given range of
phenomena. That is a matter to be tested by observa-
tion and experiment. Now it turns out that one of the
simpler ones is in close, but not exact, agreement with
the Newtonian law of gravitation Since the latter is
known to afford a close approximation to facts of ob-
servation, the covariant equation which corresponds
to it is used to define the relativistic law of gravitation.
It is that law which has brought the chief renown and
glory to Einstein, since it has conquered in the realm
of phenomena from the solar system and from regions
lying beyond the confines of the solar system. In what
way it has conquered my colleague will make known
to you tomorrow night.

Let us now review briefly the general principles
which underlie the theory of relativity in order that we
may have a clear conception of their inherent sim-
plicity. In so far as the theory differs from the classi-
cal mechanics these principles are four in number. The
first is the so-called restricted principle of relativity.
It asserts merely that the phenomena of nature run

34

A DEBATE ON RELATIVITY

their course according to precisely the same laws on
any two systems in uniform relative motion in free
space provided that either of them affords a suitable
system for the convenient expression of the laws of
nature. The second principle requires that in the
theory pf a gravitational field the first principle shall
hold as a sort of limiting condition or as a sort of
boundary condition at infinity. The third principle re-
quires that the first shall hold with an indefinitely close
approximation in an infinitesimal portion of space-
time. And, finally, the fourth demands that the laws
of nature shall be expressed in a form which is inde-
pendent of the particular reference system used, this
demand arising from the fact that there are no co-
ordinates in nature so that the coordinates should
virtually disappear from the laws of nature when ex-
pressed in their ultimate form.

One could hardly ask for a simpler basis than this
for the deepest foundations of fundamental scientific
theory. No other comprehensive theory in science
yet proposed can vie with this in the simplicity and
elegance of the fundamental basis from which it starts.
In the neighborhood of a particular event in space-
time, experiments may be carried out freely on any
small moving body, and local distances, time intervals,
pressures, densities, velocities, etc., may be treated
with security by the usual methods, applied as if the
moving body were at rest. The main elements in such
phenomena consist of a microcosmic part — the part
belonging to the local space-time — and there is only a
slight macrocosmic deviation due to the presence of
matter and the consequent curvature in the four-dimen-

FOUNDATION PRINCIPLES OF RELATIVITY 35

sional space-time continuum. Gravitational phenomena
appear as the manifestation of this curvature.

A complicated mathematical machinery, as we have
said, is necessary in working out the details of the
theory, but the basis of the analysis reaches the acme
of simplicity. Simplicity in basis and complication in
details is frequent in physical science. This is well
illustrated even in so elementary a case as the classical
theory of the tuning-fork. The general behavior, of
the tuning-fork can be theoretically explained only by
elaborate considerations , no general formula has been
found by means of which its fundamental note can be
specified in advance. To deal directly with the atoms
and electric charges of which it consists is quite im-
possible, and all we can hope to do in this direction is
to obtain geneial average effects. The detailed theory
would be enormously complicated ; the reality itself is
beyond the power of our minds to conceive adequately.
It is an illustration of the fact that there is a great com-
plication of detail in nature . “Simplicity and unity
in the fundamental processes,” as Birkhoff has said,
“and yet an infinite complexity in their combinations
seem more and more to he clearly manifested in na-
ture.”

Now you have before you the fundamental basis
of the general theory of relativity, exclusive of its ex-
tension to electromagnetic phenomena, and an indica-
tion of the nature of its detailed development. Further
into its foundations and into the problem of rearing
the Superstructure we can not go in the space of this
lecture. shall the theory be tested as to its ade-

quacy ? As in; the case of any other theory which is ac-

36

A DEBATE ON RELATIVITY

ceptable it must meet three general demands of the
human spirit, as follows : It must be in suitable agree-
ment with the facts of nature; it must have those es-
thetic qualities which render it pleasing to the human
spirit; and it must furnish what is to us the most
agreeable theory from the point of view of con-
venience. A few words must now be said about these
demands.

1 1 have already spoken briefly about the agreement
of the theory with the facts of nature. Tomorrow
night £he speakers will analyze this question in detail.

Whether the general basis of the theory is pleasing
to the human spirit depends for the present upon the
particular human spirit which is assessing it; and this
will probably continue to be true for a generation or
longer. But the whole basis of the theory is so beauti-
ful and inspiring in its simplicity and elegance and is
in such remarkable accord with the facts to which it is
applicable that it appears to be inevitable that it shall
come into general acceptance and that a future genera-
tion will understand only with difficulty how the people
of our own day often found it so perplexing. When it
was first learned that the earth is a sphere floating in
space the statement of this fact seemed to many people
to be quite absurd and out of agreement with phe-
nomena. We ourselves are today so familiar with this
conclusion that it is only with difficulty that we can
understand how the men of a former time were non-
plused by it. I confidently anticipate that the men of a
future generation will look back to our own with the
same feeling of wonder that we found it so difficult
to adjust ourselves to the point of view of the theory

foundation principles of relativity 37

of relativity. When that day comes this theory will be
quite satisfactory to the general human spirit.

How does the theory meet the demand for a con-
venient explanation of phenomena? No claim can be
made for it that it is a unique explanation. In fact, as
Poincare has so cogently shown, if there is one ex-
planation of a given body of natural phenomena then
there is an infinitude of such explanations. Hence
there is no question concerning uniqueness; it is al-
ready known that explanations are either non-existent
or are infinite in number. It becomes then a question
as to whether the theory of relativity affords the most
convenient account of the phenomena subject to its
jurisdiction; and this question, I believe, is to be an-
swered in the affirmative.

If some of you are not comfortable in the presence
of an insistence upon convenience as one of the quali-
ties which a theory should possess, let me remind you
that there is good authority for it in the writings of
such an illustrious scientist as Copernicus, who says :

“Attacking a problem obviously difficult and almost
inexplicable, at length I hit upon a solution whereby
this could be reached by fewer and much more con-
venient constructions than had been handed down of
old, if certain assumptions, which are called axioms,
be granted me.”

Now in the theory of relativity we grant ourselves
certain principles (corresponding to the axioms men-
tioned by Copernicus) and by means of these we ob-
tain a more convenient account of phenomena than
any others which have been achieved without the use
of these principles. And we are insisting upon the con-

38

A DEBATE ON RELATIVITY

venience of this procedure as being fundamental just
as Copernicus formerly insisted upon the greater con-
venience of his now immortal system than that of any
earlier theory. A chief element of this convenience
consists in the fact that we do not have to employ ad
hoc hypotheses to carry through our analysis, once we
set out from the general basis of the theory of rela-
tivity.

Here we rest our argument for the present. It has
consisted mainly in a development of the principles of
relativity in a way to make their extreme naturalness
and elegance apparent. The detailed analysis of the
experimental evidence we have left to our colleague.
Only incidentally have we shown the difficulties in-
herent in other theories ; later we shall examine what-
ever alternative principles our opponents may offer.
We shall hope to convict them of a misunderstanding of
the true nature of the theory which we are upholding,
if they should undertake merely to destroy our argu-
ment, on the ground that it is well to kill a rattlesnake
lurking in a human path even though nothing else is
put in its place. In any event, we shall return to the
discussion tomorrow night in the spirit of a genuine
search for right conclusions, convinced that to cover
dip the truth through fear or prejudice or the love of
‘victory can never be the wisest way.

THE POSTULATES OF NORMAL INTUITION

The First Speech of the Negative by Professor W. D.

M acMillan

The object of science is to coordinate and to in-
terpret our experiences with nature, and to suggest
the directions in which new experiences may be antici-
pated. This statement of aim implies a conscious mind
which is to be satisfied and the existence of something
external to it with which it has relations. We call this
external something Nature, or Reality, or the Physical
World, according to the mood we are in, but, whatever
it is, it exists apart from and independent of the con-
scious mind which perceives it. I take it that as mem-
bers of Sigma Xi we are all in agreement about this
although there are and there have been and doubtless
there will continue to be, men who assert that the con-
scious mind alone exists and that it is aware of nothing
but its own activities. It is all a dream with nothing
substantial, nothing real, back of it.

It will be perceived that I am making here my
first assumption, namely that there exists an external
reality which we call the physical world. If you do
not choose to grant this assumption you and I are in
disagreement from the start in the interpretation of
our mental activities, and there is no hope that we shall
arrive at a common conclusion. Neither of us can say
that the other is wrong, for we have no common
ground that will serve as the base of proof. We have

40

A DEBATE ON RELATIVITY

different points of view and that is the end of the
matter. It is idle for you to assert that you are right
and that I am wrong, and it is equally idle for me to
make such an assertion. I will grant that to do so
would be very human, and I think that you will grant
that it would he very childish. That procedure leads
only to quarrels and bitterness of spirit and is alto-
gether undesirable. We shall let it go and try to find
some other topic of conversation about which at least
we can start together.

The history of human relations is a long story of
quarrels and disagreements. In intellectual matters,
however, the incentive for quarreling is not great. It
does not go much deeper than the emotions of pique
and vanity, and these emotions do not make a strong
appeal to any one in his hours of reflection and medita-
tion, We are interested in living together in peace and
in profiting each by the experience of the other ; and
so when disagreement arises, if we are wise, we shall
not pursue a quarrel, but we shall try to find the ground
which we have in common; then patiently search for
the point at which divergence sets in and let the con-
versation center calmly about this point. When this
is done it is found that there are a large number of
propositions so elemental in character that we can not
get behind them, or offer any proof for the assumptions
which we make with respect to them. It is extremely
important, therefore, that we recognize the existence
and nature of these fundamental assumptions, for they
are, indeed, the foundation stones of our intellectual
structures. They are so important that they have re-
ceived a name, They are called postulates, and the

POSTULATES OP NORMAL INTUITION

41

particular collection of 'assumptions which any one
makes is called his system of postulates.

Let me give another example of a postulate, one
that is familiar to every one, though, perhaps, not by
that name. We recognize that most, if not all, physi-
cal things have a beginning in time, and an end also.
The question arises — does the physical universe as a
whole have a beginning? or, in common language,
was it created? Many people make the postulate that
it was. Scientists usually make the postulate that the
physical universe had no beginning and therefore that
it has always existed. As evidence on the matter is out
of the question, one is free to choose either postulate
and he is perfectly safe in his choice from the assaults
of either evidence or logic. Scientists do not make
the postulate that the physical universe was created for
the simple reason that, for their purposes, such a pos-
tulate is utterly barren. If one wishes to assert that
the physical universe was created this morning at
8 o’clock Central Standard Time, no one can success-
fully dispute him. If you say that you remember what
happened yesterday, or last week, or last year, the
answer is that your memories were created with you.
If you say that the erosion of the continents and the
fossils in the rocks indicate the lapse of many ages,
you are confronted with the reply that the earth was
created that way. and you are helpless. Of course, if
one wishes to have his postulate say that creation
occurred six thousand years ago or six million years
ago, or a billion times six million years ago, he is per-
fectly free to do so. You may wonder why, with un-
limited freedom, he should choose any particular time ;

42

A debate on relativity

but whatever date he does choose you can not say that
he is wrong. It is easy to see, therefore, why scientists
in general do not make such a postulate. It does not
help them in the explanation of anything. For their
purposes it is barren and sterile and therefore useless.

It will be helpful, I think, to dwell a little longer
upon the postulates that are commonly made with
respect to this external reality which we sometimes call
Nature, sometimes the Physical Universe, sometimes,
perhaps, other names. It will be observed that I say
they are commonly made. I do not say that they have
been agreed upon, for such is certainly not the case.
Intellectual men are very little disposed to agree about
anything where disagreement is possible, and the do-
main of the postulates is precisely that domain in which
they are perfectly free. I shall state these postulates
as though they were facts, but any one who is so dis-
posed may assert exactly the opposite without starting
a quarrel.

The physical universe is continuous in time. This
postulate asserts that the universe had no beginning
and will have no end. It is at this point that we part
company with many of the theologians.

The physical universe is not hounded in space . To
say that it has no boundaries is equivalent to saying
that it is infinite in extent.

There exist physical units, which for finite intervals
of time preserve their identities and exhibit character-
istic properties. Examples of these units are electrons,
atoms, molecules, crystals, cells, stars, galaxies.

The sequence of physical units is infinite both ways.
That is to say, there is no largest physical unit mi

POSTULATES OF NORMAL INTUITION

43

there is no smallest one.

The phenomena of nature occur always in- such a
way that certain relations remain invariant. This is
merely a technical way of saying that processes of na-
ture are orderly and that, therefore, science is possible.
Any one who assents to this postulate, and sticks to it,
is essentially a scientist. Any one who asserts the con-
trary, whatever else he may be, is not a scientist.

The energy within a region of space does not in-
crease or decrease unless there is a corresponding de-
crease or increase in some other region of space. This
is the doctrine of the conservation of energy and com-
mands almost universal assent.

The universe does not change always in any one di-
rection. That is, the universe does not flow like a
stream from one unknown region into another. It is
more like the ocean which, while never twice alike, is
yet always the same.

I will mention only two more postulates, although
many more could be set down.

The geometry of the physical universe is Euclidean.

The time of the physical universe is Newtonian.

This is the fork in the road where the modern
school of relativity branches off. We must stop, there-
■fore, and see what these postulates mean.

We must distinguish between the geometry of in-
tuition and a mathematical geometry, or the space of
intuition and a mathematical space. The space of in-
tuition is the normal three-dimensional space in terms
of which we are all accustomed to think. The geom-
etry which has been built up from our intuitions is
the geometry of Euclid, the geometry that is taught in

44

A DEBATE ON RELATIVITY

all of our schools. After having learned through our
intuitions how to build up such a mathematical sys-
tem, it is possible to vary the postulates on which the
system is founded and to build up abstract geometries
by means of pure logic. Such geometries are called
non-Euchdean, and the corresponding spaces are called
non-Euclidian spaces. They do not agree with the
space of intuition, and the theorems with respect to
them are the conclusions of a cold visionless logic. It
is perhaps a misnomer to call them geometries at all,
but whatever name is applied to these mathematical
systems, our common Euclid belongs in the class.

According to the great geometer Riemann, there are
infinitely many of these geometries. It all depends
upon how the length of a curve is defined. Let us have
a simple illustration. Suppose we had a metal plane,
say of copper, which was indefinitely great in extent.
Suppose further, that this plane was hotter in some
spots than in others, and that our measurements on this
plane were made with a thin steel ruler. The tempera-
ture of the ruler would vary as it was moved about on
the plane, and its length also would vary with the tem-
perature. The length of the ruler would depend upon
where it was. It is needless to say that under such
circumstances the familiar proposition of Euclid that
the sum of the squares on the two sides of a right tri-
angle is equal to the square on the hypothenuse would
not be verified and the ratio of the circumference of
a circle to its diameter would not he the well-known
number v. It would not even be constant as measured
by the steel ruler. Its value would depend upon where
the center of the circle was and how large the diameter

POSTULATES OF NORMAL INTUITION

45

was.

This is all simple and intelligible enough. But a
mathematician will say, “Give me the coefficient of ex-
pansion of your ruler and the distribution of tempera-
ture over the plane and I will devise for you a geo-
metry that will fit that plane. It will be necessary no
longer for you to speak or think of variations in tem-
perature. A special non-Euclidean geomerty is what
you want.” This is true enough and such a geometry
might be helpful, but you and I who are accustomed
to dwell in a physical world will prefer to think of
the geometry of that plane as Euclidean and to ascribe
the failure of our measurements to verify the theorems
of Euclid to physical causes rather than to think in
terms of a non-Euclidean geometry with which we can
compute, but for which we have no intuitions. Doubt-
less the reason for this is that of all these infinitely
many geometries the Euclidean is the simplest. The
experience of the race has shown that we can always
think in terms of it and charge the failures of our
measurements to physical causes. It is not because the
Euclidean geometry is truer than the non-Euclidean;
it is not because the Eculidean geometry is intrinsically
bound up with the physical universe; it is because it
is simpler for us to impose the Euclidean geometry
upon it and to think in terms of Euclid and of physical
causes than to think in terms of an infinite variety
of special geometries. This has been true throughout
the long history of our race, and it is for this reason
that oar intuitions are Euclidean.

Let me take another example, this time from as-
tronomy. In Euclid’s geometry it is possible to draw

46

A DEBATE ON RELATIVITY

only one line through a given point parallel to a given
line. In Lobachevski’s geometry it is possible to draw
infinitely many, and in Riemann’s geometry it is im-
possible to draw any at all. In Lobachevski’s geometry
the parallax of every star, however distant, is positive
and greater than a certain small number. In Euclid’s
geometry they are positive, but have the limit zero as
the distance increases. In Riemann’s geometry they
are all negative. Let us appeal now to experiment.
Let us measure the parallaxes of the stars and then de-
cide. The experiment is very difficult and we are just
able to make the measurements. The answer is not
decisive Some parallaxes, as measured, are negative,
but we ascribe these results to errors of observation.
As for the others, the greatest is 3/4", while the others
seem to have zero as a limit, but the errors of observa-
tion are relatively great and we can not be sure. But
even if they had all turned out negative we should not
have adopted Riemann’s geometry. We should simply
have concluded that light, for some reason or other,
did not travel in a straight line. There would have
been a choice, and, as has always been the case, the
trouble would have been thrown, not upon geometry,
but upon physics.

Speaking upon this subject some twenty five years
ago the great French mathematician, geometer, and
physicist, Henri Poincare, said : “Can we maintain that
certain phenomena which are possible in Euclidian
space would be impossible in non-Euclidian space, so
that experiment in establishing these phenomena would
directly contradict the non-Euclidian hypothesis? I
think that such a question can not seriously be asked.

POSTULATES OF NORMAL INTUITION

47

To me it is exactly equivalent to the following, the
absurdity of which is obvious: — There are lengths
which can be expressed in meters and centimeters, but
which can not be measured m feet and inches.”

Finally, in order to bring the matter within the
range of the average man’s comprehension, it was
shown that a dictionary could be constructed by means
of which the theorems in the geometry of Lobachevski
and Riemann could be translated into the theorems of
the ordinary geometry of Euclid, and vice versa. The
mystery of these non-Euclidian geometries is now
clear. They are merely different languages. What-
ever can be said in Russian can also be said in English.
We who have been raised to speak the English tongue
are not going to trouble ourselves about speaking Rus-
sian just because we have recently discovered that a
Russian language exists. We shall be quite content
to believe that whatever we may have to say can be
said in our own language.

I have dwelt somewhat at length upon the non-
Euclidian geometries because their discovery about a
hundred years ago by Lobachevski, a Russian, and by
Bolyai, a Hungarian, created great excitement among
the mathematicians of that time, and the question at
once arose • which of these geometries is the true geom-
etry? But after a hundred years of meditation upon
the subject the excitement has largely died out, and
from a practical point of view the matter has been
summed up by Poincare in the statement: “Euclidian
geometry, therefore, has nothing to fear from fresh
experiments.”

In our own times a new excitement has arisen

48

A DEBATE ON RELATIVITY

among the mathematicians. Einstein has discovered a
non-Newtonian mechanics, and immediately the fight
is on : “Which is the true mechanics?” The mechanics
of Newton, like the geometry of Euclid, was based
upon our normal intuitions and it is, therefore, in-
telligible in the normal sense of the word, just as Eu-
clid is intelligible. The geometry of Euclid is the
foundation upon which the mechanics of Newton is
reared. If to the subject of geometry are added the
concepts of time, mass, and force and new postulates
are added to state how these new concepts are to be
measured, the new intellectual structure which arises
is the subject of mechanics. These new concepts of
time and force can not be defined, but they can be
measured. Newton stated postulates by which this
can be done, and these postulates are familiar under
the name — Newton’s Laws of Motion. Not only did
Newton lay down these new postulates, but he de-
veloped the mathematical machinery that is necessary
for tracing out the consequences of these new ideas.
In the two hundred and fifty years that have elapsed
since his work was first published, the subject of me-
chanics has been enormously developed upon the basis
which he laid down. It has been the guide to all of our
engineers in the marvelous achievements of modern
times. It has furnished the ground work for all of
our interpretations in the domain of physics, and, com-
bined with Newton’s own law of gravitation, it has
explained the motions of the members of our solar
system with such exactness that the subject of Celestial
Mechanics seems almost to have attained that goal
which is one of the aims of every science, namely,

POSTULATES OF NORMAL INTUITION

49

complete and accurate prediction.

Newton conceived of time just as do all the rest of
us. He thought of time as flowing onward, continu-
ously and uniformly, alike for all; and therefore
“Newtonian time” is sometimes called “public time”.
Whether a person be busy or idle, active or passive,
awake or asleep, m Indiana or on the planet Mars,
time flows on unceasingly and the same instant of time
arrives everywhere simultaneously, irrespective of lo-
cal physical conditions. It can be measured in different
units such as days or years, just as distance can be
measured in yards or miles. The particular unit em-
ployed is not material, but the time itself is the same
everywhere.

At the very time when Galileo and Newton were
laying the foundation of mechanics, studies were in
progress as to the nature of light, and the great dis-
covery was made in 1676 by the Danish astrono-
mer Roemer that light does not travel instantaneously
from one point to another, but that it travels at a cer-
tain speed which, while very great — 186,000 miles
per second- — is not infinite. Even in Newton’s day
there were two theories as to the nature of light. The
Dutch physicist Huyghens regarded light as a wave of
some kind, while Newton regarded a beam of light as
a stream of very small corpuscles which were emitted
by a luminous body. The masterly exposition of the
corpuscular theory by Newton and the great authority
of his name maintained that theory in a dominant po-
sition until the beginning of the 19th century when the
work of Young in England and Fresnel in France
completely displaced it and gave to the undulatory

so

A DEBATE ON RELATIVITY

theory a dominance which it has held to the present
time. According to this theory all space is filled with
an ether which has the properties of an elastic solid,
and light consists of transverse vibrations, like the
waves on a stretched string, in this medium. Notwith-
standing the properties assigned to the ether, large
solid bodies, like the earth, move through it without
disturbing it in any way.

Another field in the domain of physics came into
existence early in the 19th century with the study of
the phenomena of electricity and magnetism. The
master investigator in this field was Michael Faraday.
The ideas of Faraday were developed and put into
mathematical form by Clerk Maxwell something more
than sixty years ago. Maxwell showed that things
happen just as though there existed at every point in
the neighborhood of an electrical charge two forces,
an electrical force and a magnetic force, just as the
law of gravitation states that at every point in the
neighborhood of every particle of matter there exists
a force which we call gravitation. It was found
further that the ratio between the electrostatic unit
and the electromagnetic unit was, within the limits
of experimental error, the velocity of light in the ether.
This led Maxwell to perceive that an electromagnetic
disturbance would be propagated in free space with
the velocity of light, and to conclude that light was
merely an electromagnetic disturbance. Thus the
theory of optics and the theory of electricity which had
not been previously suspected of having any relation
to each other, were joined together in a more compre-
hensive theory — the theory of electro-magnetism.

POSTULATES OF NORMAL INTUITION

51

The success achieved by this theory in accounting
for all the known phenomena in its domain has been
very great. It seemed about to rival in its perfection
the attainments in the domain of Celestial Mechanics
until Michelson performed, in 1887, what he himself
has called his “unfortunate experiment”. Just as the
science of Celestial Mechanics rests upon a set of
equations which result from the laws of motion and the
law of gravitation, so the electro-magnetic theory rests
upon a set of equations given by Maxwell, who re-
garded the electromagnetic disturbances as being pro-
pagated in an all pervading ether. The two sets of
equations, dealing as they do with two quite different
'classes of phenomena, are naturally not at all alike.
But there is one difference between them which has a
philosophical significance. There is no suggestion that
gravitation is propagated at all; or if one wishes to
think of propagation, its speed is infinite; and the
law of gravitation does not mention propagation. As
a consequence of this the equations of Celestial Me-
chanics, which describe the motions of the planets of
our solar system relative to the sun, remain unchanged
whether the solar system is regarded as being at rest
relative to the general system of stars or whether it
is regarded as being in uniform motion along a straight
line with any speed whetever. The equations of mo-
tion being just the same for the two cases there is no
phenomenon in the system which would distinguish
one case from the other. This is the old-fashioned,
Newtonian relativity, which is quite agreeable to the
philosophical instincts of most people, A point of ab-
solute geometric space has no meaning.

52

A DEBATE ON RELATIVITY

It is different, however, with the equations of elec-
tro-magnetism. These were based upon the concept
of an ether which fills all space and which has many
of the properties of an elastic solid. A point which
is fixed relative to the ether can be regarded as fixed
relative to absolute geometric space, since the ether is
not regarded as moving relative to absolute space. The
velocity of propagation of the electro-magnetic waves,
including light, being constant relative to the ether,
can not be constant relative to bodies like the earth
which do not have uniform straight line motion rela-
tive to the ether. Relative to such moving bodies the
electro-magnetic equations are not the same as they are
at rest relative to the ether. Since the equations are
different one would expect the phenomena to depend
upon absolute motion with respect to the ether.

The very great speed with which light is propa-
gated, however, makes these differences, which depend
upon the square of the velocity of light, extremely
minute. Nevertheless they should be measurable, just
as the parallaxes of the stars are measurable. Very
difficult, to be sure, but still measurable. Michelson
tried the experiment of measuring the motion of the
earth relative to the ether with his newly invented in-
terferometer, but the results were negative. The ex-
pected phenomena did not appear. He could find noth-
ing to measure. Others tried similar experiments, but
the results were the same ; nothing that was expected
appeared. It was a great blow to the theory, and the
mathematical physicists were in great distress.

A few years later Fitzgerald and Lorentz showed
that these failures could be accounted for by supposing

POSTULATES OF NORMAL INTUITION

53

that all bodies moving through the ether contracted by
an extremely small amount in the direction of the mo-
tion, the amount of the contraction varying as the
square of the velocity of the body (about two and one
half inches for the diameter of the earth) , but the sug-
gestion seemed artificial and it did not satisfy. It
seemed that the electro-magnetic equations, like the
gravitational equations, should be independent of uni-
form motion with respect to the ether. Larmor and
Lorentz succeeded in finding a transformation which
did leave the equations unaltered, but it was less sim-
ple than the transformation required for a body mov-
ing uniformly in a straight line, in that it transformed
not merely the position of the body but its time also.
In this way was introduced the concept of a “local
fictitious time”, and relative to this local fictitious time
the electromagnetic equations actually are invariant.
The local fictitious time depends upon how fast the
body moves with respect to the ether.

It was at this point that Einstein appeared with the
remark that this local fictitious time was the only kind
of time we know anything about. In fact, it was actu-
ally our real time, and what we had previously re-
garded as real time was actually the fictitious time.
This remark inverted the problem. Relative to New-
tonian time, the gravitational equations were invariant
while the electro-magnetic equations were not. Rela-
tive to Einstein’s time, the electro-magnetic equations
are invariant while the gravitational equations are not.
The pinch of the shoe was transferred from one foot
to the other, and Einstein boldly followed up the con-
sequences.

54

A DEBATE ON RELATIVITY

In the special theory of relativity which followed,
Einstein was interested only in the electro-magnetic
equations Not only were the experiments of Michel-
son and Morley accounted for by this new point of
view, but several other results that previously had been
explained with difficulty were now explained very
simply and no new difficulties of a measurable char-
acter were encountered, But it played havoc with the
fundamental concepts of the entire human race. Time
is no longer a public matter, the same for all, but is a
private, personal matter Your time and my time are
different, just as your personality and my personality
are different. Two events, one in New York and one
in Chicago, are simultaneous in my time, but if you
are moving with respect to me these two events will
not be simultaneous in your time. The speeds of two
bodies which are moving in the same straight line are
not additive. For example, if you are riding on a train
which is moving relative to the track at a speed of 36
miles per hour and you are walking forward on the
train with a speed of four miles per hour, your speed
relative to the track will not be 40 miles per hour, but
will be something less than that. A beam of light trav-
els with a speed of 186,000 miles per second relative
to its source. A normally-minded man would say that
j£ two beams of light are travelling in opposite di-
reetions the speed of each relative to the other is twice
186,000 miles, but the relativist replies : ‘‘No ! it is only
.486,000 miles. It is just the same as though one of
them stood still. A speed greater than the speed of
||g^t is impossible."

You and I regard a five pound mass as a five pound

POSTULATES OF NORMAL INTUITION

55

mass for eveiyone. To the relativist that is not so. It
depends upon whether you are standing still or run-
ning If you run fast enough it will be a ten pound
mass, and if your speed is that of light, its mass will
be infinite. Furthermore, there exists a definite rela-
tionship between mass and eneigy — namely, one gram
of matter is equivalent to the square of the velocity of
light ergs of energy.

It lequnes a great deal of courage to talk like this
to sane people, but nevertheless these are the logical
consequences of Einstein’s postulates. Of course, the
meaning of the word “time” has slipped a bit and the
meanings of the other words have slipped with it so
that it is not quite fair to make these statements to an
unsophisticated person But if you can change your
notion of time and make the corresponding change in
the meanings of the other words it will be found that
the statements are correct You will observe that it is
like translating English into Russian. It doesn’t
sound quite right in Russian, but as usual that is be-
cause we do not clearly comprehend the meanings of
the words

Einstein’s special relativity ignored the fact that
these new concepts were upsetting the equations of
gravitation. People were so busy trying to learn this
new language that they forgot all about this fact, or
perhaps they never perceived it. But Einstein neither
overlooked it, nor forgot it. He was meditating, try-
ing to enlarge his notions so that both systems of equa-
tions should be independent of the reference system.
Other mathematicians came to his assistance and in the
geometry of Riemann and the calculns of tensors of

56

A DEBATE ON RELATIVITY

Ricci and Levi-Civita, together with a postulate of his
own, which he called the Principle of Equivalence, to
the effect that a gravitational field of force is indis-
tinguishable from any other kind of field of force, he
found the means of formulating his problem. The law
of gravitation which emerges is not quite that of New-
ton, and a great variety of laws is possible. To all of
them Newton’s law is an extremely close approxima-
tion so that these laws give results in our own solar
system which are indistinguishable from those of New-
ton except in one place, namely, the motion of the peri-
helion of Mercury. The law which is usually used was
first given by Schwarzschild and it indicates an ad-
vance in the perihelion of Mercury of 43" of arc per
century greater than that indicated by Newton’s law.
Now it happens that there were two small discrepan-
cies between the implications of the Newtonian theory
and the observations. One of these is a slight irregu-
larity in the motion of the moon, and the other is that
the perihelion of Mercury is advancing 43" per century
faster than the theory indicated. Einstein’s theory
would explain one of these, and the explanation is in-
credibly perfect, but not the other. There are several
other suspected discrepancies, but they are so small
that they cannot be discussed with any certainty. That
Eintein’s law of gravitation should fit one of these dis-
crepancies so perfectly and ignore the others altogether
is a bit puzzling. But naturally the relativists seize
upon this one agreement as a striking confirmation of
their procedure.

There are other predictions which the new theory
makes. A ray of light passing close to the edge of the

POSTULATES OF NORMAL INTUITION

57

sun should be deflected from, its straight line course by
a definite amount. A careful test of this prediction
was made by the Lick observatory and the prediction
was confirmed. Another prediction was that the lines
of the spectrum coming from a large body like the sun
should be shifted towards the red, and this, too, after
much trouble, has been affirmed by St. John at the
Mount Wilson observatory where the instrumental
equipment is of the very best. Thus the three predic-
tions originally made by Einstein have been affirmed,
at least roughly. Naturally the relativists are elated,
and I think they have a right to be. In addition to
these three definite predictions of Einstein the theory
of relativity applied to the Bohr atom has been useful
in interpreting the fine structure of certain lines in the
spectrum, and possibly in other places. These success-
es of the theory have made some of the followers of
Einstein over confident, sometimes even arrogant and
irritating in their assumption of lofty superiority. A
certain measure of success can be freely granted to the
doctrine without for a moment assenting to the philos-
ophy which underlies it, and I think it has been very
successful in making mathematical formulas.

It will be granted, I think, that the law of gravita-
tion has been very successful in the making of formu-
las. Indeed, it has always been regarded as the best
verified of all physical laws, and it was not invented by
Newton. The idea was current in Newton’s time that
the. law of gravitation is the inverse square law because
gravitation was supposed to be something like radia-
tion and the law of radiation is obviously the inverse
square law. Newton deduced the law from Kepler’s

58

A DEBATE ON RELATIVITY

three laws of planetary motion and showed that it is
equally applicable to the motion of the moon. He stated
it in its present form, and so it is naturally called New-
ton’s law. The underlying concept of radiation which
first gave mathematical form to its expression was
abandoned even by Newton himself. The formulas
derived from it, however, remain as accurate and use-
ful as ever.

Newton was able to explain many of the properties
of light on the hypothesis that light consists of minute
corpuscles which are emitted by the luminous body.
But a hundred years later. Young and Fresnel suc-
ceeded in explaining the same phenomena and many
new ones on the hypothesis that light is a wave motion
in the ether. So numerous and so successful were
these explanations that it became almost a dogma that
light is a wave motion in the ether. But the recent
work of Compton and others has brought into evi-
dence phenomena that can not, apparently, be ex-
plained by the wave theory.

The electro-magnetic theory was based upon the
concept of an ether, and it is the relativists themselves
who put the ether into the discard This is one of the
defects of the doctrine of relativity, for it does not
say anything about how light is propagated. Both the
emission theory and the wave theory give clear notions
on this point. They may not be adequate, but the doc-
trine of relativity gives us nothing at all.

In the second century A. D. the astronomer Ptolemy
m writing his book, the Almagest, which was the bible
of the astronomers for fifteen hundred years, was
called upon to decide between the geocentric and the

POSTULATES OF NORMAL INTUITION

59

heliocentric theories of the solar system. Both theor-
ies were well known, but Ptolemy decided against the
heliocentric theory, which has been the standard theory
for the past three hundred years, because he could ob-
serve no paiallax for the fixed stars. If the earth
moves around the sun there should be a relative dis-
placement of the stars among themselves with a period
of one year. Since he could find no evidence of such
a displacement, he concluded that the earth is station-
ary and that the sun moves around the earth. Fifteen
hundred years later the telescope was invented and
with this powerful addition to their equipment the
search for the parallax was renewed, but again no
parallax could be detected. More than two hundred
years passed away before their search was rewarded.
A star does have a parallax after all. But how differ-
ent is the scale of the sidereal universe from that which
Ptolemy had anticipated.

In the days of Newton the parallax had not yet been
found. Suppose Newton in constructing his dynamics
had made it a postulate that the parallax did not exist,
and suppose further that he had succeeded in building
up a Celestial Mechanics in which the earth was at
rest relative to the stars. How much more compli-
cated would such a system of mechanics have been,
than if he had proceeded, as he did do, by ignoring the
parallax altogether, and had followed his intuitions
with respect to time and space and force. It was just
one hundred and fifty years after Newton published
the Principia that the parallax of the stars fitted into
his scheme as a matter of direct evidence.

We of the present generation are too impatient

60

A DEBATE ON RELATIVITY

to wait for anything. Within thiity years of Michel-
son’s failure to detect the expected motion of the earth
with respect to the ether we have wiped out the slate,
made a postulate that by no means whatever can the
thing be done, and constructed a non-Newtonian me-
chanics to fit the postulate. The success which has
been attained is a marvelous tribute to our intellectual
activity and our ingenuity, but I am not so sure with
respect to our judgment. Our normal mode of pro-
cedure is to assume that a ceitain something is true or
to guess that a certain thing can be done, and then to
test our assumptions and guesses by experience. I
think I am safe in saying that the vast majority of our
hypotheses find their way promptly to the waste bas-
ket and are forgotten. Occasionally one is found that
meets with a certain measure of success and we are
elated with it, only to find later that it won’t do and it
is laid aside with regret. On rare occasions one is
found, like Newton’s law of gravitation, or the electro-
magnetic theory, that seems to be a permanent acquisi-
tion of the race. But there are grave difficulties even
with the best of them. I think I am also safe in say-
ing that no physical hypothesis will do more than har-
monize approximately our system of postulates and
our experience, or, to use more popular language, no
physical hypothesis is more than an approximation to
the truth. Nature is infinitely complex and therefore
we have only to push our experience far enough to find
that our physical laws are imperfectly stated, and that
our physical models are inadequate.

It is not our normal mode of procedure to assume,
after two or three failures, that by no means whatever

POSTULATES OF NORMAL INTUITION

61

can the thing be done. It is particularly distasteful to
do so when such an assumption involves the conclusion
that our experience can no longer be interpreted in
terms of the time and space of our intuitions, and that
we have accordingly reached the limits of what is in-
telligible.

The notion of simultaneity in two distant places
according to Newtonian mechanics is not ambiguous,
as is so frequently asserted by the relativists. We can
set two distant clocks to indicate the same time with a
certain margin of error. That there is a lower limit to
this error merely asserts that our intellects are more
delicate than our physical apparatus. However fast
or slow light may go, we can imagine a speed a million
times as great, or any other ratio that may be desired,
and there is no lower limit, save zero itself, to the de-
termination of simultaneous events so far as the mind
is concerned. To say that simultaneity does not exist
because it is unattainable in practice is like saying that
a straight line does not exist because it, too, physically
is unattainable. Shall we then put geometry into the
discard because it is ambiguous and without meaning?
If we do the matter is ended, for there is nothing left
for us to talk about.

The process of idealization is a fundamental proc-
ess in all of our thought. Our ideals are the norms in
terms of which we think and without them there will
be no thought at all. Some set of ideals is indispens-
able. So far as I can see our normal set of ideals,
which include Euclidian space and Newtonian time,
is not an exclusive one. Other sets are possible, per-
haps infinitely many, but I can see no reason for

62

A DEBATE ON RELATIVITY

believing that some other set is better than the one with
which nature has endowed us. As the non-Euclidian
geometries of Riemann and the non-Newtonian me-
chanics of Einstein, which is merely a non-Euclidian
geometry in four dimensions, clearly show, we can
trace the application of these ideals by the rigid pro-
cesses of logic, but our intuitions, which are the eyes
of all our thoughts, are blind, and I am sure that we
shall not go very far without our eyes. So far as I can
see, such schemes are entirely possible, but I feel quite
sure that they are futile. The relativists have gathered
a few flowers in the dark, but I am afraid we shall
wait a long time before they have gathered an armful.

It will be observed that in the preceding discussion
I have granted all of the claims of the relativists, and
still I have denied their conclusion that the relativists
are the sole dispensers of the truth and that we must all
become relativists. The situation is something like
that of a boy and his bed clothes. The boy grew but
the bedclothes did not. All at once the boy discovered
that his little toes were sticking out from under the
covers and he was decidedly uncomfortable. Try as
he would the bedclothes could not be stretched far
enough to cover them up. Suddenly he had a bright
idea. All he had to do was to slip the entire bed covers
down six inches. His feet went under beautifully and
he was so happy about it that it took him some time to
discover that now his neck was uncovered and that he
had merely shifted the seat of the difficulty for the bed-
clothes were no longer than they were before. The
relativists have succeeded in covering up the little
terms of order two, but in doing so they have robbed

POSTULATES OF NORMAL INTUITION

63

us of all ideas as to how light is propagated in space)
and that problem is even more important than the little
difficulties at the other extremity.

The experimental evidence, however, upon which
the relativists have laid so much stress, is not so clear
as one might wish. In granting that the evidence is all
that the relativists could wish it to be I have granted
too much. This part of the discussion will be taken
up by Professor Hufford who will show that the evi-
dence is very obscure. To me, however, the evidence
is not a decisive matter. It is quite likely that each of
the two schemes can be modified so as to cover the
evidence, whatever it may be. If this estimate is cor-
rect, the mechanics of Einstein will, from a philoso-
phical and a historical point of view, occupy a position
beside the geometry of Lobachevski, and the human
race will continue, as before, to think in terms of Eu-
clidian space and Newtonian time.

IS THE EXPERIMENTAL EVIDENCE OF
RELATIVITY CONCLUSIVE?

The Second Speech of the Negative by Professor
M. E. Hufford.

In surveying the progress of physics during the last
century one is impressed by the method of its growth.
The first step is the statement of a principle or hypothe-
sis more or less new in departure, and the second step
is a searching experimental investigation of the truth
or falsity of the theoretical statement. At the present
time we have before us the theory of relativity, still,
in the estimation of most physicists, in the theoretical
stage. It is true some observations and experiments
have been made and important ones arc sure to fol-
low. However, many experimental physicists feel
that our investigations in the laboratory are too few
and our astronomical observations far too limited to
prove and establish relativity fully.

It is my purpose to discuss the so-called experi-
mental triumphs of the theory of relativity and to point
out some instances wherein these fall short of proof.
It is an occasion also to point out other requirements
which the theory must meet in order to take its place
along with those great principles like the wave theory
of light, the theory of the electron constitution of
atoms and others which are the substantial framework
of science.

At the outset it is clear that relativity is very closely

IS THE EXPERIMENTAL EVIDENCE CONCLUSIVE? 65

associated with the theories of light. In fact the hy-
potheses of relativity arose in an effort to account for
a difference between theory and experiment in that
field. Let us consider briefly, therefore, some im-
portant advances in the concepts which underlie that
subject which were made in the years between 1675
and 1750. This was one of the most important periods
in the history of physics for during this time the
foundations of our present day ideas of the nature of
light and the manner of its passage through space were
laid. In 1675 Newton communicated his theory of the
corpuscular nature of light in which he encountered the
difficulty of accounting for the gradual reduction in in-
tensity at the edge of shadows. Huyghens in 1690 ac-
counted for the bending of light by assuming a wave
method of propagation. Roemer, just before this
period, had satisfactorily proved that light does not
have an infinite velocity and in 1728 Bradley made
his celebrated observations on the angle of aberration
of the fixed stars. Since the Bradley experiment is
the starting point for the situation in which physics
found itself at the time of the announcement of the
Einstein theory we may stop a moment to consider it.

If a ball thrower should throw a ball toward a
moving railway car in which the windows were open, it
is possible to imagine that the speeds of the car and
the ball might be such that the hall could enter the
front window on one side and pass out at the last
window on the opposite side. Now a passenger on the
car and the thrower would disagree as to the direction
in which the ball actually moved. The passenger
would certainly maintain that the ball was thrown in a

66

A DEBATE ON RELATIVITY

direction diagonally across the car. In the case of the
Bradley experiment the observer corresponds to the
passenger and if he is to direct his telescope so that
light from a star is to pass down the axis of the tube
he must point his instrument ahead of a straight line
connecting himself and the distant star. Six months
later, when the earth is moving in the opposite direction
in its orbit, he must direct his telescope at the same
angle in the opposite direction. It is easily seen that
the ratio of the velocity of light to the velocity of the
orbital motion is the tangent of the angle of aberration.
Bradley and astronomers until recent years have ac-
counted for the results of this experiment on the basis
of a stationary or, as we customarily say, a stagnant
ether.

Now all went well unHlhiew^Kenomaha were dis-
covered and then arose the conflict which today we are
attempting to explain by relativity. The phenomena
referred to were those involving a slowing up of the
velocity of light in media which are denser than air
and the fact that blue light suffers greater decrease in
velocity than the red. Fresnel offered as an explana-
tion of these phenomena the idea that the ether in mat-
ter is denser than the free ether. It is easy to see,
therefore, that if the Bradley telescope tube were filled
with water the angle of aberration should be increased.

This experiment was tried by Airy and Hoek and
strange to say the angle of aberration was not changed.
Of course it is possible that the matter filling the tube
may drag the ether along with it just enough so that
the velocity change by altered density of the ether is
just compensated for. This gives rise to an ether-drag

IS THE EXPERIMENTAL EVIDENCE CONCLUSIVE? 67

theory. Fresnel derived a law in which the velocity, u',
of the ether, that is the drag velocity, in relation to the
velocity u of dragging matter, was expressed by the
formula :

«'=(!- 3) «.

The Airy-Hoek experiment required, then, that the
ether filling the tube have greater density than that
outside and that either the ether inside is permanently
attached to the tube and that tube and all move
through the free ether like a tube filled with jelly
moves through a basin of water, or else that the ether

flows in at one side and out at the other crossing the
tube with a speed less than that of the tube.

In 1859 Fizeau in France devised an experiment to
test the law of the drift of the ether with matter which
had been proposed by Fresnel. As shown in Figure 1,
light from a source S fell upon a mirror set at 45°.
From the mirror two beams of light passed through
a lens, thence through apertures and through a water-
filled tube. Another lens and mirror then caused the
light beams to return through the tube, the paths be-
ing interchanged. It will he seen that the one beam
traveled through the water in both directions with the
flow of water, while the other moved against the

68

A DEBATE ON RELATIVITY

stream. At the point of observation the crests and
troughs of the light waves of the two beams came to-
gether in such a way that a system of interference
bands was produced. Now when one of the beams was
retarded over the other the whole system of bands
move across the field of view. The arrangement
was an exceedingly delicate one, and by it Fizeau
found that when the speed of water reached two meters
per second he could observe the shift while with seven
meters per second he could measure it. This experi-
ment was repeated by Michelson and Morley at Cleve-
land in 1886 with precisely the same results. Appar-
ently the correct conclusion to be drawn from the ex-
periment is that an ether exists and that transparent
matter carries the ether with it to a measurable extent.

Fresnel’s theory also supposes that the ether out-
side of transparent bodies remains stagnant. To test
this part of the theory was the aim of Michelson and
Morley in their work published in 1887. This is the
experimental work known as the Michelson-Morley
experiment. It was Einstein's effort to explain the
negative result obtained which in part gave rise to
relativity.

Light from a source S in Figure 2 was divided by
a mirror set at an angle of 45°. The two beams trav-
eled over paths D and D' of an interferometer at right
angles to each other. After retraversing the paths the
light was reunited so that interference fringes were
produced Any retardation of light in one path over
that in the other was indicated by a shift of the fringe
system. Since the velocity u of the earth in its orbit
carries the apparatus forward as shown by the broken

IS THE EXPERIMENTAL EVIDENCE CONCLUSIVE? 69

lines, the effect is to increase the path D' over the path
D by an amount D u 2 /c 2 where c is the velocity of light.
When the apparatus is rotated through 90° the effec-

O

Figure '2.

tive difference in path is doubled. Michelson and
Morley predicted a fringe shift of 0.4 of a band, but

70

A DEBATE ON RELATIVITY

the experiment yielded less than l/20tli of a band.
The Michelson-Morley experiment may be interpreted,
therefore, as showing that, contrary to Fresnel’s hy-
pothesis, the ether is carried along with the earth with
a velocity between 3/4 and 5/6ths of the earth’s veloc-
ity.

Due to the importance of the experiment as de-
ciding against a fixed ether which so well explained
the Bradley experiment, Lord Kelvin at the Congress
of Physics at Paris in 1900 suggested that the experi-
ment should be lepeated with still more sensitive ap-
paratus. This Morley and Miller undertook to do in
1904 and 1905. The fringe shift expected with im-
proved apparatus was 1.5 bands. These experimenters
announced as a result of the repetition, that if the ether
moves past the earth it is with a velocity less than 3.5
kilometer per second ; that is, the ether is carried along
with 7/8 or 9/10th of the earth’s orbital velocity.

Not completely satisfied that the small positive re-
sult was due to experimental error, Miller in 1921 to
1925 has repeated the experiment at Mount Wilson
and again at Cleveland. The reason for choosing
Mount Wilson, where the elevation is 6,000 feet above
sea level, was to see whether or not there is greater
relative motion of the ether at greater distances from
the surface of the earth, In all, 12,500 determinations
have been made. The apparatus was used in such a
way that a minimum fringe shift indicated the direction
of the resultant motion of the earth in space and the
maximum shift indicated the magnitude of the relative
motion of the earth and ether. The measurements have
been grouped so that all the data of a group have the

IS THE EXPERIMENTAL EVIDENCE CONCLUSIVE? 71

same conditions as regards the known motions of the
earth.

Figure 3.

From D. C. Miller in Science,

The curves of Figure 3 show the results of meas-
urements made during 1925 on the direction of the

r-*yd"

IS TIIE EXPERIMENTAL EVIDENCE CONCLUSIVE? 73

relative motion. While the earth remained approxi-
mately at a given position in its orbit, that is during a
day, the apparatus was rotated as much as 20 turns per
hour and the direction in which a minimum fringe shift
occuired was noted. The ordinates of the small dots
of the curves represent the angle at which a minimum
occuired. The heavy line represents average angles.
The curves of Figure 4 show the relative motion of
the earth and ether as calculated from the maximum
fringe shift Here the ordinates represent kilometers

From Proceedings of the National Academy of Sciences.

per second of difference of velocity of the earth and
ether. While there is considerable variation it is clear
that a definite drift velocity is indicated.

These same results are shown in another way in
Figure 5. Here the circumference of the circle repre-
sents a sidereal day. The magnitudes of the ether-
drift values determined at different hours of the day
are represented by the lengths of the arrows and the
directions of the arrows indicate the direction of the

74

A DEBATE ON RELATIVITY

drift. While the results of 1925 show more variation
of direction still it is clear that there is a general drift
toward the north west. The fact that the results of the
two periods agree inspires our confidence and we must

admit that Miller has found a definite velocity of drift.

Miller made a careful search for a direction
and magnitude of motion of our solar system which,
when compounded with the known revolution and ro-

IS THE EXPERIMENTAL EVIDENCE CONCLUSIVE? 75

tation of the earth and projected upon the plane of the
interferometer would give a curve representing mag-
nitude and direction like Figures 3 and 4 obtained
by experiment. It has been found that an assumed re-
sultant drift motion in the direction of the constellation
Draco of magnitude ten kilometers per second, gives
projections which agree remarkably well with experi-
ment. The curves of figure 6 show this agreement.
The light-line curve represents the general average of
experimental results and the heavy-line curve repre-
sents assumed magnitudes and directions. In all of
Miller’s experimental work he found that the earth’s
orbital motion is without effect on the results. If,
therefore, it is assumed that the earth’s orbital motion
is a component of the drift velocity which is just below
the limit of the resolving power of the interferometer,
then in order to obtain the drift velocity of ten kilo-
meters per second, which is only a residue, so to speak,
of the true velocity in space that is masked by the large
drag of the ether by the earth, the other component of
motion must be a velocity of 200 kilometers or more
per second in the direction of the constellation Draco.

It does not seem possible to attribute any of these
results to experimental or other errors. In taking the
data every precaution was used to remove the errors
which might be caused by the mechanical disturbances,
heat effects and magnetic effects. Mirrors were
changed, observers were shifted about, even the build-
ing was moved and differently oriented.

These results are, therefore, a serious challenge to
the theory of relativity, because in that theory one of
the postulates is that the velocity of light in free

76

A DEBATE ON RELATIVITY

space is constant and is independent of whether we
assume the presence of an ether or not. It should be
pointed out, also, that one of the important conclusions
of relativity is that, whether the ether is assumed to
exist or not and whether it is stagnant, drifts, or is
carried along, it is not possible to detect any motion of
the earth in space by means of light.

The experimental physicists now leave it to those
theorists, who accounted for a supposed null result of
the Michelson-Morley experiment by relativity, to see
whether that theory can satisfactorily account for
Miller’s results. The challenge is a serious one to
those who have faith in relativity. The outcome will
mark an epoch in science.

I wish to discuss anolher experiment which has been
regarded by some mathematicians and physicists as a
complete verification of the theory of relativity. In
an effort to explain the null result of experiments like
the Michelson-Morley experiment, FitzGerald first
proposed that material bodies, when in motion, actually
diminished in size in the direction of their motion.
Einstein has introduced into his theory certain postu-
lates which, when followed to their logical conclusions,
also lead to this same principle. Accordingly we have
the expressions :

m,=^ , and rm ,

where m (i represents the mass of the body when at
rest, mi the mass when it is moving parallel to the rela-
tive velocity of the two systems, one of which con-
tains the moving body and the other the observer ; m (

IS TIIE EXPERIMENTAL EVIDENCE CONCLUSIVE? 77

represents the mass wh,en the motion of the body is at
right angles to the relative motion of the systems; (3
is the ratio of the relative velocity of the systems to
the velocity of light. From these formulas it is clear
that the mass of a body is larger when it is in motion
than when it is at rest. The expressions also say that
if the speed of the body becomes equal to that of light
its mass becomes infinitely great.

This change of mass with velocity was tested in
the Kauffman-Bucherer experiment. The apparatus
consisted of parallel circular plates A and B, Figure 7.
placed very close together. At X a small amount of
radium fluoride ejected electrons whose speeds were
nearly that of light. Electrons spread out in all di-

Figure 7.

rections and fell on a circular film which completely
surrounded the plates at some distance from thgm.
The impression of the electrons on the film made a
black line. Then, with an electric field perpendicular
to the plates and a magnetic field in the plane of the
plates, the high speed electrons were caused to travel
over a spiral path between the edge of the plate and
the film. If, then, the mass of an electron, due to its
speed, is so great that it is not deflected by the magnetic

Md. and the value of M. la

found from simple calculation that the traces of the
electrons with field on and field off should coincide at

78

A DEBATE ON RELATIVITY

positions around the film 180° apart. A maximum
difference should be shown at points half way between.
Figure 8 is a reproduction of the photograph obtained
in this way.

While the result of the experiment is very beautiful,
indeed, we are impelled to examine the assumptions.
We can arrive at exactly the same form of equations
as those just mentioned if we assume, instead of a vari-
ation in mass, a variation of the charge of electricity
carried by the electron. In fact, one of the postulates
of relativity states that the sum total of electricity in
any isolated system remains unaltered. We have a
right to question the truth of this postulate, and we can

Figure 8.

From A. H Buchcrer, Annalen der Physik

not conclude that relativity has been established until
we have established the truth of this statement by ex-
periment. This may be a difficult problem for we
measure charge only by its effects and it is conceivable
that the medium of transfer of the effect might be
subject to change with a variation of the velocity of
the charge. In a recent paper by Bush, 1 it has been
shown that all of the relativity equations result from
an assumption of constant mass and changing charge
just as we now have them by postulating a variable
mass and a constant charge. It has been stated by one

„ .’'Bulletin of Massachusetts Institute of Technology, vol
S* fio, 3, p. 129.

IS THE EXPERIMENTAL EVIDENCE CONCLUSIVE? 79

of the ablest mathematical supporters of relativity
that if the relation

e/ = e«,i/ i — p 1

is found for charge, the whole theory of relativity will
be overturned, and if any relation, except a constancy
of charge, is found the theory must undergo modifica-
tion. 2

2 R. D. Carmichael: The Theory of Relativity, second ed.,
(1920), p. 70.

Let us turn attention now to another of the so-called
proofs of the Einstein theory. This is the advance-

*' if, i

ment of the perihelion of the planet Mercury'?' It is
well known that the orbits of the planets are ellipses.
That portion of the ellipse nearest the sun is called the
perihelion, It has been observed that the orbit of Mer-
cury slowly rotates about the sun. Leverri er com-
puted the path of Mercury, taking account of the at-
tractions of the earth, Venus, Jupiter and three other
bodies. He found that the actual and calculated mo-
tions failed to agree by an amount which would be near-
ly 38 seconds of arc per century. Leverrier could not
understand this discrepancy and suggested that there
might be unknown masses of matter near the sun. Since
that time some matter has been found and exactly
where Leverrier predicted that it should be. In 1895
Newcomb repeated the calculation and by slightly re-
ducing the eccentricity of the orbit he slightly increased
the rotation and obtained 41 seconds per century.

Now Einstein by the use of the equations of rela-
tivity has calculated that the perihelion of Mercury
should rotate 43 seconds per century due to the sup-
posed change in space and time in the neighborhood of

80

A DEBATE ON KELATIVITY

the mass of the sun. It has been pointed out by Pro-
fessor Poor that, in making these calculations, Einstein
failed to use his relativity unit of time, but used instead
our constant Newtonian unit of time. The agreement
between the calculated values of Leverrier and New-
comb on the one hand, and of Einstein on the other has
been considered definite proof of relativity. But it
must be remembered that Newcomb was forced to
guess the density of Mercury and the other planets.
Hence the figure 41 may be far in error. Since the so-
called verification by the calculations of Einstein, the
rotation of the perihelion of Mercury has been recal-
culated and values of 33 and 29 have been announced.
We have here a variation of 27 per cent.

In a recent issue of the Proceedings of the Physical
Society of London, J. T. Combridge 1 has a mathemati-
cal paper on the shift of the perihelion of Mercury. In
that paper it is shown that if we take the equations of
Newtonian mechanics and add a potential function, we
can get the Einstein equation for the orbit of a planet.
This yields possibilities of explaining the shift of the
perihelion of Mercury as well as the bending of rays
of light by the sun without resort to the Einstein pos-
tulates and equations at all. The author states that
there are endless possibilites of "explaining” the “cru-
cial” phenomena of Einstein’s theory without appeal
to that theory. It is pointed out in the paper that the
motion of the perihelion of Mercury depends upon only
one of the ten coefficients in Einstein’s quadratic form.
We need, therefore, for a crucial test as between Ein-

, '^Proceedings London Physical Society, vol. 38, (1926),

p. 161,

IS TIIE EXPERIMENTAL EVIDENCE CONCLUSIVE? 81

stein’s theory and the Newtonian equations with an
added potential function, a phenomenon which involves
more than one of the coefficients. We must have a
wider search for further possibilities of experimental
investigation.

Another obseivation which has been considered a
triumph for relativity is the bending of a ray of light
which passes near a massive body. By assuming a
strained condition in space accompanying a localization
of energy and that these strains experience resistance
when in motion, it is concluded that energy and mass
are one and the same thing. Light energy is, on these
assumptions, subject to the gravitational action. If,
therefore, a beam of light passes close to the sun’s limb,
it should be attracted by the sun and its path curved.
Substitution of values in the relativity equations shows
that the maximum bending of beams from stars seen
just at the edge of the sun should be 1.75 seconds of
arc. Of course to make measurements of the displace-
ment it is necessary to utilize the few minutes during
a solar eclipse. Two opportunities for such obser-
vations have occurred. Observations were made by
British astronomers who were sent on an expedition
to South Africa in 1919 and the Lick observatory sent
an expedition to Australia in 1922. Both parties
brought back positive results. These results have been
accepted by relativists as a complete verification of
their theory.

But in examining the conditions of the observations
and the results, one wonders whether the proof is so
complete. In the first place, both Professor Edding-
ton who headed the British party and Professor Camp-

82

A DEBATE ON RELATIVITY

bell who was in charge of the American group are en-
thusiastic relativists and one must wonder whether
they approached their problem with entirely unbiased
minds. In the second place it has been shown that 0.87
seconds deflection, that is half of the computed amount,
should be expected on the basis of the Newtonian
corpuscular theory.

Since the advent of Planck’s quantum theory of
energy a great deal of interest has been restored to
the Newtonian corpuscular theory. Sir J. J. Thom-
son during the past year has published several papers
in which he has attempted to credit the corpuscular
theory, that is, the quantum theory, along with the wave
theory of light. According to Thomson’s view a part
of our light energy exists in the form of waves, while
another part exists in the form of corpuscles or light
quanta. Here again we need more experimentation

But even on the basis of the wave theory we should
expect a bending of light both at the surface of the sun
and again when a beam enters our own atmosphere.
This is the ordinary refraction phenomenon. We
know something about the refractive properties of the
Jower layers of our own atmosphere, but we know
much less about the rare upper layers and still less
about the dense layers of atmosphere of the sun. To
be able to say just how much a beam of light, which is
of magnetic and electric nature, should be bent in pass-
ing through a very intensely hot atmosphere composea
of very heavy gases and vapors, ionized and un-ionized,
attracted by a body of great mass surrounded by strong
gravitational and magnetic fields, is, indeed, difficult.
It must be remembered, too, that when our earth passes

IS THE EXPERIMENTAL EVIDENCE CONCLUSIVE? 83

into the shadow of the moon, as it does during an
eclipse, when our bending measurements are made,
our atmosphere suffers great cooling and, therefore,
contraction and change of density. These changes are
sure to be accompanied by changes in refraction. Also
when radiation from the sun is cut off our atmosphere
loses its ionized state in the upper layers. With all
of these changes the problem of understanding the
bending of the sun’s rays during eclipse is, indeed,
difficult.

The apparent displacements due to bending of light
by the sun, as computed on the basis of relativity, are
shown in Figure 9. The photograph is from a drawing
by Professor Poor. Figure 10 is a photograph of a
drawing of the actual displacements of the stars by
Professor Poor. These displacements were made from
the data of the Lick observatory astronomers. In both
of these photographs, one theoretical and the other
from the data of observation, Professor Poor has
multiplied the displacements by a given constant factor.
It wiill be observed that in some cases the bending near
the sun was far less than was expected and some of
the beams farther out are bent far too much. Fifteen
of the star images show bending in the predicted direc-
tion and twenty-six show a deviation exactly opposite
to that required by relativity. Out of these complicated
displacements Professor Campbell deduced results and
announced 1.72 seconds as the observed displacement.
A re-calculation, however, showed 2.05 seconds. This
is a 17 per cent variation from the amount predicted.
No experimental observation can be regarded as de-
cisive with such a large difference as this, and especially

84

A DEBATC ON RELATIVITY

when the difficulties of observation and the extremely
limited time are taken into account.

Within a few years we have heard much about the
verification of relativity by the shift of the lines toward
the red region in the spectrum of the light from a
massive body. Such a shift is predicted on the basis
of slower time on a large mass accompanied by lower
frequency of oscillation of electrons in producing light.
With slower vibrations the corresponding spectrum
lines appear farther toward the red. This is an effect
like that produced by a source rapidly moving away
from an observer, thus increasing the wave length of
the light. A shift produced by motion is a Doppler
effect. Now Einstein’s equations show that the mass
of the sun should produce an increase in the wave
length of light equal to .008 of an Angstrom unit, that
is 8X IT 11 cm. increase over the same wave of light on
the earth. Attempts to measure this very small shift
have proved unsatisfactory. At the suggestion of Pro-
fessor Eddington attention has, therefore, been di-
rected toward the much denser faint companion star of
Sirius. In Sirius and its companion we have a
most interesting combination. We know the relative
velocity of the two bodies. We know what to expect
from the Doppler principle. The mass of the faint
companion is equal to that of our sun. Spectrum
analysis and absorption effects show that its tem-
perature is 8,000°. The intrinsic brightness of the
star is low although it is called the White Dwarf. This
is interpreted as indicating small size. Hence the den-
sity as computed by Eddington is 50,000 times that
of water. Our earth is 5.5 times that of water. With

IS THE EXPERIMENTAL EVIDENCE CONCLUSIVE? 85

these data the Einstein shift amounts to .3 Angstrom
units, an amount well within the reach of our instru-
ments.

At the meeting of the American Association for the
Advancement of Science, at Kansas City, in January,

« 9

0

4- *

Figure 9.

From C. L. Poor in The Forum Magazine.

St. John from the Mount Wilson observatory showed
photographs of the spectrum lines of light from the
star Sirius and a comparison spectrum of the light
from the faint companion. The shift of the lines in
the latter spectrum was clearly shown and was of the

86

A DEBATE ON RELATIVITY

magnitude predicted by relativity.

It seems necessary to experimentalists in drawing
a conclusion from observations like those given by St.
John to take account of other possibilities which might
explain the facts. In such a high temperature the

4 N \

From C. L. Poor m The ForuiH Magazine.

atoms concerned with the origin of the light must be
broken up, that is, ionized singly, doubly, etc. ; it would
be difficult to tell to what extreme extent. There is
a very heavy atmosphere about such a dense hot body.
This would produce layers of gas and vapor which

IS THE EXPERIMENTAL EVIDENCE CONCLUSIVE? 87

would refract the light. There is probably also a
strong magnetic field about the companion star.
No one can tell what line-shift may occur when a
source of light is placed in a legion of such high tem-
perature, great pressure and intense magnetic field
Such conditions are most difficult and perhaps im-
possible to reproduce in the laboratory. There may,
therefore, be other ways of accounting for this phe-
nomenon than to say that the atomic vibrator is slowed
up because it is placed on a massive body where time
moves slower.

We have had a very interesting attempt at verifica-
tion of relativity in an experiment undertaken on a
large scale by Michelson and Gale near Chicago. In
this experiment a twelve-inch pipe line a mile in length
was laid in the form of a rectangle (See figure 11).
By a system of pumps the air in this line could be
reduced. Light was sent in at one corner of the rect-
angle. It was divided by a mirror and one beam was
passed around the tube in one direction and the other
around in the. opposite direction. The two beams were
brought together again in such a way that interference
fringes were formed. Any change in velocity of the
light due to the earth’s orbital motion affects one of the
light beams more than the other. This effect is indi-
cated by a displacement of the interference fringe sys-
tem. A fringe shift of .236 of the width of a band was
expected on the basis of calculation. A fringe shift was
obtained. Sometimes it was large, sometimes small.
Out of a large number of very varied results an aver-
age value of .230 was deduced. The relativists claim
this as a proof of their theory, but it has been shown

THE EXPERIMENTAL VERIFICATION OF
RELATIVITY

Concluding Arguments of the Affirmative by Professor
H. T. Davis

In the last analysis a physical theory must survive
or perish at the hands of the experiments . No matter
how much it may appeal to our reason or stimulate our
imagination the real test of whether it exists merely
as a fancy of the mind or represents an interpretation
of physical fact must come from the laboratory. Im-
manuel Kant has sought to reduce experience to a
subjective basis and in doing this his space and time
have become shadowy creations which forever elude
us in the strange mystery of the source of a priori
knowledge. There is something much more satisfying
to the mind in referring the mystery of space and time
to an objective reality in which knowledge is not al-
ready inherent in the mind, awaiting some slowly
evolving revelation, but presents a challenge to experi-
mental science. Ernst Mach, whose ideas on the rela-
tivity of motion were ahead of his time, has put it
thus: "Mathematical and physiological research has
shown that the space of experience is simply an actual
case of many conceivable cases, about whose peculiar
properties experience alone can instruct us.”

I should like, first, to call your attention to an ex-
periment that, for all its simplicity, nevertheless is
one that has profound inplications. In 1852 Jean

EXPERIMENTAL VERIFICATION OF RELATIVITY 91

Foucault hung in the pantheon at Paris a spherical
pendulum and demonstrated that the axes of the ellipse
described by the bob revolve around the vertical in the
direction east-south-west-north with the angular ve-
locity ft sin (f> where ft is the angular velocity of the
earth and <f> is the latitude in which the experiment is
performed. If the pendulum is set to swinging at the
north pole the axes of the ellipse described by the bob
will have the angular velocity of the earth as we meas-
ure it by reference to the external framework of the
fixed stars, but if the pendulum is removed to the
equator then no such motion can in any way be de-
tected. How can we explain this experiment? It
means this, that the pendulum can be used to detect an
absolute acceleration of matter in space, but can never
detect what we might think of as an absolute velocity.
Every point in a plane tangent to the earth at the north
pole and rigidly fixed to it is subject to an accelera-
tion directed toward the pole, but on the equator every
point in a tangent plane has a constant, that is to say,
an unaccelerated velocity equal to 1500 feet per second.
What Foucault’s pendulum does is to detect the ac-
celeration, while it leaves the velocity absolutely undis-
covered.

In making these statements one should point out
the rather curious fact that the absolute rotation of
the earth corresponds within the limits of experimental
error to its rotation as determined by referring to the
framework of fixed stars. The space-time continuum
in the neighborhood of the earth, however, is suffi-
ciently different from the space-time in vacuo that a
secondary effect should appear, according to Professor

92

A DEBATE ON RELATIVITY

Eddington, in the rotation as determined on the one
hand by reference to the fixed stars and on the other
by the Foucault pendulum. As the estimated effect is
only 1.94" per century this prediction is beyond the
reach of experimental verification.

After we have reflected upon the very surprising
fact that by no mechanical means can we detect an
unaccelerated velocity, although accelerations even of
small order are readily found, it does not require an
unusual generalization to arrive at the principle that
velocities are outside of our experimental range even
when light pulses or any other physical phenomena are
used to find them. For example, aberration tells us
with great accuracy our orbital velocity, which like the
velocity of rotation is an accelerated one, but gives no
answer at all to the perplexing question of where and
how fast we are travelling in space itself.

In an interesting paper on the subject L. Silberstein
has considered the problem of “the Rotating Earth as
a Reference System for Light Propagation” and has
pointed out that one of the principal features of the
theo'ry of relativity is the close connection established
between the behavior of mechanical and optical phe-
nomena. 4 “In fact, .... whatever the quadratic dif-
ferential form determining the metrical properties of
a world domain, its geodesics prescribe the motion of
the free particles, and the minimal lines of the same
metrical manifold express the propagation of light in
vacuo”. The Michelson-Gale experiment, which will
be described later, was devised to test the agreement
of optical phenomena on the earth with this principle
Philosophical Magazine, vol. 48 (1924), pp. 395-404.

experimental verification of relativity 93

It is interesting to observe that the discovery of the
inertia of energy follows directly from this point of
view, which is a simplification of physical principles
that is greatly to be wished for.

In the light of these remarks the experimenter
might, perhaps, postulate relativity like this:

I. Unaccelerated velocities are not absolute proper-
ties of physical bodies, but are derived from relative
positions in space and time.

II. Accelerations are absolute properties of physi-
cal bodies and can be objectively determined.

I should like to refer next to an experiment which
was performed a short time ago by Professor Michel-
son and Professor Gale of the University of Chicago. 5
A line of twelve-inch pipe something over a mile in
length was laid near Chicago in the form indicated by
the accompanying picture. The air was then pumped
out until a vacuum was formed in which the air re-
sistance was less for the entire path of more than 6,000
feet than would be encountered in 100 feet of air at
normal pressure. Two beams of light were then sent
in opposite directions in the pipe over the circuit
ADEF, reflected around the corners by mirrors, and
reunited so as to produce interference fringes at A.
As a mark from which to measure the displacement a
second set of fringes were formed by reflecting light
beams around the shorter course, ABCD. Now it will
be evident that if the apparatus were stationary in the
ether which conveys the light, the two beams would
come together without producing an interference fringe
since they would then travel equal paths in the same
c The Astrophysical Journal , vol. 61 (1925), pp. 137-145.

94

A DEBATE ON RELATIVITY

EXPERIMENTAL VERIITCATION OF RELATIVITY 95

length of time. If, on the other hand, the line of pipe
had a motion through the ether, the case would be
altered. It turns out that by any theory the orbital mo-
tion of the earth would not produce any effect m the
interference of the light. The rotation of the earth,
however, is a different matter. In one direction the
mirrors would be advancing to meet the light while in
the other they would be receding from it. If the pipe
line had been laid all around the earth this would be
more evident, but in the actual experiment the differ-
ence in velocities at points of different latitudes was the
effect made use of.

There are three possibilities to be examined in this
experiment. Some scientists explained the lack of ef-
fect in the original Michelson experiment by assum-
ing that the ether which conveyed the light was
dragged along by the walls of the laboratory. As I
understand Professor Miller’s recent experiment this
is one of the conclusions that he wishes us to reach
since he obtained comparatively large interference
fringes at the top of Mount Wilson and very slight ef-
fects in his laboratory at Cleveland, which would indi-
cate a partial drag. This is called the “ether-drag”
theory and I shall so refer to it. On this assumption
the ether in the heavy pipes at the altitude of Chicago
should be carried along by the apparatus and no inter-
ference would then be detected.

A different result, however, would be expected on
the basis of the “ether-wind’ or “ether drift” theory,
which assumes that the ether is extremely tenuous and
forms a huge, stagnant ocean through which the earth
and all material objects move without disturbance.

o.o 5

96

A DEBATE ON RELATIVITY

We see that on this hypothesis the ether moves through
matter much as the air would pass through the meshes
of a screen carried on a swiftly moving car. It is easily
proved that the shift on this basis would be ,236 of a
fringe or 1/200,000 of an inch, an amount well within
the experimental range of the interferometer.

Curiously enough the theory of relativity, which
asserts that accelerations, but not velocities, are de-
tectable by interference fringes, leads to exactly the
same predicted shift as that obtained by the ether-
drift theory. These calculations are made, of course,

Fringe Displacement
Figure 12.

From the Astrophysical Journal,

on. the basis of a space-time element ds, computed for
the neighborhood of the rotating earth. A detailed
analysis of the considerations which enter will be found
in The Theory of Relativity , Second edition, (1924)
by L. Silberstein, p. 376 et seq. We have, therefore
no way of distinguishing between the ether-drift anc
the relativity theory on the basis of this experiment
although the fundamental hypotheses are very differ-
ent since the one assumes that the shift measures a ve
locity, while the second assumes that it results from at

EXPERIMENTAL VERIFICATION OF RELATIVITY 97

acceleration due to the rotation of the earth.

The picture, (Fig. 12) shows the results of the ex-
periment which give .230 for the mean value of the
shift, the difference between this and the predicted
value being well within the error of the instrument.
This experiment, I feel, is a very serious challenge to
the ether-drag conclusion arrived at by Professor Mil-
ler and must cast doubt upon his conclusions until there
is some way of reconciling the two experiments.

I shall next discuss in turn the three deductions
from Einstein’s theory of relativity which so surprised
the world of science when they were announced and
which have subsequently received such notable verifi-
cation.

The first of these is an explanation of a fact long
known, but never adequately explained. Mercury, the
small planet near the sun, has a peculiar advance in the
perihelion of its orbit that can not be accounted for on
the basis of Newton’s theory of gravitation except by
the assumption of the existence of a large quantity of
matter in the neighborhood of the sun. This undis-
covered matter has been long sought for, but never
found. I can not go into the details of the intricate
discussion aroused by this point, but it is sufficient to
remark that the discrepancy between observation and
theory is beautifully and exactly accounted for by the
theory of relativity. For Mercury there is an advance
of 43" per century and the difference between the rela-
tivity calculations and observations is .58" with a prob-
able error of .29". Professor Eddington in his
Theory of Relativity (p. 90) makes the following
remark: “Einstein’s correction to the perihelion of

98

A DEBATE ON RELATIVITY

Mercury has removed the principal discordance ill the
table, which on the Newtonian theory was nearly 30
times the probable error. Of the IS residuals 8 exceed
the probable error, and 3 exceed twice the probable
error — as nearly as possible the proper proportion.

Figure 13.

From Lick Observatory Bulletin, No. 34 6

But whereas we should expect the greatest residual to
be about 3 times the probable error, the residual of the
node of Venus is rather excessive at 4 y 2 times the
probable error, and may, perhaps, be a genuine dis-

EXPERIMENTAL VERIFICATION OF RELATIVITY 99

cordance. Einstein’s theory throws no light on the
cause of this discordance ”

One of the most spectacular predictions made by
Professor Einstein was that of the bending of light in
the neighborhood of the sun The only way m which
this could be tested was by making observations at the
time of the eclipse and comparing the observed and cal-

fWU

ty-

culated positions of the stars. According to Einstein,
light that just grazed the hmb of the sun should be
deflected 1 75", which is twice that predicted by New-
tonian theory. The accompanying photographs show
the results obtained by the Crocker Eclipse Expedi-
tion to Wallal, Western Australia, 1922, You will ob-
serve m the first picture, (Fig. 13), that the stars near

100

A DEBATE ON RELATIVITY

the sun’s limb are deflected further than those at a
greater distance and it may be calculated that the mean
deflection is the value predicted by Einstein within the
limits of experimental error. In the second picture,
(Fig. 14), the dotted line is the theoretical displace-
ment and the broken line connects the group means of
the observed displacement.

The third prediction, which had to do with the dis-
placement of spectrum lines in heavy stars, was for a
long time in doubt and Einstein maintained that the
validity of his entire theory of gravitation depended
upon the truth or falsity of this third crucial test. I
must first explain to you that the velocity with which
distant stars are moving toward or receding from us
can be measured by the displacement of lines in the
spectrum. This is known as the Doppler effect and is
analogous to the change in pitch of a locomotive
whistle as the train is moving toward or away from us.
Now according to Einstein’s theory, in the neighbor-
hood of heavy bodies a Doppler effect should be ob-
served as a result of the difference between earth and
sun time which arises from the change in the four
dimensional space-time continuum of the two bodies.
On the sun, due to its great mass, time moves some-
what more slowly than on the earth. Hence an atom
on the sun would vibrate more slowly than an atom on
the earth and this would appear to us as a Doppler
shift toward the red end of the spectrum. For the sun
this effect is very small, amounting for a wave length
of 4000 Angstrom units (10~ 10 m.) to a relative dis-
placement of only .008 of a unit, which is approxi-
mately 32 trillionths of an inch. This we could in-

experimental verification of relativity 101

terpret as a recessional velocity ol .63 kilometers per
second except that we know that no such velocity ex-
ists. For a long time observations using the utmost
power of available instruments were made in order to
detect this shift, but the effect was so close to the limits
of observation that little confidence was felt one way
or the other.

However, C. E. St. John after a long study of the
problem finally concluded in a paper published in 1923
that such an effect does exist on the sun. The follow-
ing table shows the agreement between the calculated
and observed wave lengths for various groups of lines
studied :

Group No

of Lines Mean Wave

Calculated

Observed

Length

Shift

Shift

a

17

3826

.008

.012

b

24

3821

.008

.0112

b

10

4308

.0091

.0113

a

10

5419

.0115

.0112

b

95

4166

.0088

.0072

b

36

6294

.0133

.0115

d

106

4763

.0100

.0069

a

33

4957

.0105

0074

"The

conclusion

is,” says.

St. John, 0

“that three

major causes are producing the differences between so-
lar and terrestrial wave-lengths, and that it is possible
to disentangle their effects. The causes appear to
be the slowing up of the atomic dock in the sun to an
amount predicted by the theory of generalized rela-

°On Gravitational Displacement of Solar Lines, Monthly
Notices of Royal Astro Society, vol. 84, (1923), pp, 93-96. See
also Proceedings of National Academy of Science , vol. 12
(1926), pp. 65-68,

102

A DEBATE ON RELATIVITY

tivity, radial velocities of moderate cosmic magni-
tude and in probable directions, and differential scat-
tering in the longer paths traversed through the solar
atmosphere by light coming from the limb of the sun.”

Because of the exceedingly small shift in the sun’s
spectrum, astronomers turned to the sky to find some
other object which might serve the purpose better in
verifying or discrediting the prediction. Very fortu-
nately such an object exists in the double star formed
by Sirius, the dog star, and the small sun that accom-
panies it. This companion, the White Dwarf as it is
sometimes called, is one of the most remarkable objects
in the heavens since, although only one ten-thousandth
as bright as Sirius, it has about 2/Sth of its mass and
is tremendously dense, this density reaching the amaz-
ing figure of 50,000 times that of water. This figure
is all the more fantastic when we remember that the
earth is only 5.5 times as dense as water.

Because some people have difficulty in believing
that an object as dense as this really exists, it is both
interesting and important to review the arguments by
which one arrives at such an astounding conclusion. 7

In the first place we know from observation that the
period of rotation of the visible star is 49.3 years and
that the major axis of the path of the companion is 20
earth-radii, From Kepler’s third law we may deduce
without difficulty the following formula :

4 3 77 2

M/JW = (^) (^) ,

where M is the mass of the double star, T the period
of one of the components, and A the major axis of its
’See Eddington, Monthly Notices, vol, 84 (1924), p. 308.

EXPERIMENTAL VERIFICATION OF RELATIVITY 103

orbit ; M' the mass of the sun and earth, T' the period
of the earth, and A ! the major axis of the earth’s orbit.
Upon substituting the known values in this formula,
we find that the mass of the double star is approxi-
mately 3.5 times that of the sun. But we can measure
not only the path of the companion but also the path of
both stars relative to the center of gravity of the sys-
tem. This leads to the conclusion that Sirius has a
mass 2 l /> times that of the sun and that the mass of the
dwarf, consequently, is equal to that of the sun.

In the face of this conclusion a surprising thing is
now observed. At a distance of nine light years away
the white dwarf is a star of only 8.5 magnitude,
which, in less technical language, means that it appears
to be only 1 /376th as bright as our sun. This, of
course, is not so surprising until we learn from a study
of the dwarf’s spectrum that it is considerably hotter
than our sun, having, as a matter of fact, a surface
temperature of about 8,000° as compared with 5,900°
for our sun. The Stefan-Boltzmann law of radiation
states that the total radiation of energy per unit vol-
ume is proportional to the fourth power of the abso-
lute temperature of the radiating body. Hence the
surface brightness of the dwarf must be actually
(80/59) 4 =3.34 times that of the sun.

The facts, then, appear to be these : that the dwarf,
while having the same mass as the sun and a surface
brightness three and a third times as great appears to
be a star only l/376th as bright as our sun. The ob-
vious conclusion that we can draw from these figures
is that the dwarf has a surface only 1/1256 as large
as that of the sun and hence must have a radius only

104

A DEBATE ON RELATIVITY

.028 as large as the radius of the sun. This leads im-
mediately to the conclusion that the density of the
dwarf must reach the enormous figure of 50,000 times
that of water as has already been stated.

Now in the neighborhood of a star of this great
density, space and time would be quite different from
the space and time in the neighborhood of a body like
our sun or like Sirius, so a large Einstein shift toward
the red end of the spectrum was to be expected. As a
matter of fact the shift as predicted would be as great
as .3 of an Angstrom unit as compared with .008 for
the sun and this is well within the limits of our instru-
ments.

You will now recall that such a shift can be inter-
preted in two ways : first, as an Einstein shift, or sec-
ond, as a recessional velocity in space. In order to
show that it is a true Einstein shift, photographs were
taken under great technical difficulties at Mount Wilson
of both Sirius and the companion at a time when
they were moving with a velocity of 1.7 kilometers
with respect to one another. Upon comparing the
faint lines of the spectrum of the dwarf with the
nearly eclipsing spectrum of Sirius a shift was ob-
served slightly larger even than the one calculated by
Professor Eddington. If the shift is not an Einstein
shift then one alternative explanation is that the com-
panion is moving away from Sirius with a velocity of
more than 20 kilometers per second which we know is
not the case.

In commenting upon these results 8 W. S. Adams,

^Relativity of Displacement of the Spectral Lines in the
Companion of Sirius. Proceedings National Academv of Sci-
ence, vol. 11 (1925), pp. 382-387.

EXPERIMENTAL VERIFICATION OF RELATIVITY 105

who was responsible for the details of the experiment,
makes the following remarks :

“Although such a degree of agreement [between
predicted and observed values] can only be regarded
as accidental for observations as difficult as these, the
inherent accord of the measurements made by differ-
ent methods, and in particular with the registering
microphotometer, is thoroughly satisfactory. The re-
sults may be considered, therefore, as affording di-
rect evidence from stellar spectra for the validity of
the third test of the theory of general relativity, and
for the remarkable densities predicted by Eddington
for the dwarf stars of early type of spectrum”.

Attempts have been made to explain this shift by
other means, one explanation being that it is due to
pressure, but the spectrum lines used in the experiment
are those which are known to be unaffected by pres-
sure. Thus we see that this prediction of Einstein,
which for a long time was regarded by relativists as
the greatest source of danger to the theory, has proved
in the end to give a verification as complete as can be
expected under present methods of experimentation.

There are various other experiments supporting the
relativity theory which I can only mention in passing.
Trouton and Noble sought to determine a motion of the
earth through the ether from an expected torque ex-
erted on a suspended electrical condenser by the ether
wind. No such effect was found. This experiment
has recently been repeated by R, Tomaschek 8 on the
Jungfrau in the Alps at an altitude of 11,342 feet
(3457 meters) again with negative results. The

B Annalen der Physik, vol. 78 (1925), pp. 743-756.

106

A DEBATE ON RELATIVITY

bearing of this experiment upon the results obtained
by D. C. Miller in his recent drift experiments upon
Mount Wilson will be referred to later.

Lord Rayleigh 10 and later D. B. Bruce 11 with a
more sensitive apparatus sought in vain for a change
in orientation of the optical axis in a body when the
axis was changed from a position horizontal to the
direction of the earth to a direction perpendicular to
it. This was a conclusion consistent with relativity
since the discovery of such a change would have led
to the discovery of an absolute velocity in the ether.

The fine structure of spectrum lines is beautifully
accounted for by Professor Sommerfeld as an effect
due to relativity . 12 We believe now that the phenom-
enon of the occurrence of lines in light spectra is
caused by the motion of the electrons in the matter
which is emitting the light. We also believe that the
electrons are all moving in their orbits within the atoms
with high velocities, so that the relativity effect upon
their motions should be very much greater than that
found in the motions of bodies like the earth and the
planets where the velocities are comparatively low.

Suppose, then, that one of these electrons is mov-
ing in an elliptical orbit about its sun, the so-called nu-
cleus or proton of the atom. The relativity effect
would then exhibit itself in an advance in the perihelion
of the orbit of the electron. In other words the diam-
eter of the ellipse would move forward with every
revolution of the electron and its two extremities

10 Philosophical Magazine, 6th ser., vol. 4 (1902). p. 678.

11 Philosophical Magazine, 6th ser., vol. 7 (1904), p. 317.

12 Atomic Structure. English Translation (1923), Chapter

EXPERIMENTAL verification of relativity 107

would trace out the arcs of concentric circles as illus-
trated in figure 15.

Using the hypothesis of the quantum theory which
says that the energy radiated or absorbed by an atom
is determined by abrupt jumps of the electrons from
one possible orbit to another, we find that the rela-
tivity effect actually appears in a measurable way in the
formulas which determine the spectrum lines of the
radiation. This effect exhibits itself as a fine division
of spectral lines which, without taking account of the

relativity hypothesis, should have appeared as single
lines. This fine structure in the Hydrogen spectrum
has been completely verified by experiment and, ac-
cording to Sommerfeld, gives “ocular evidence not only
of the actual occurrence of the elliptic orbits, but also
of the variability of the electronic mass.”

The subject of the aberration of light has already
been mentioned, but since the phenomena connected
with this theory are exactly and simply accounted for
by the principles of relativity I shall take a few mo-

108

A DEBATE ON RELATIVITY

merits to present the argument. My colleague has al-
ready mentioned that the addition of velocities follows
a new law. We no longer can say with Newton that a
man who is walking three miles an hour down the aisle
of a railroad coach moving at the rate of 30 miles
an hour is moving with a velocity of 30+3 miles an
hour with respect to the earth. We must say with
Einstein that he is moving with the velocity of

30+3

1+30X3/C 2

where c is the velocity of light. In other words ve-
locities are compounded according to the formula
(h+I/)/(1+« U/c ~).

The entire theory of aberration follows from this sim-
ple consequence of the theory of relativity.

Thus our opponents have explained to you that
when a beam of light is sent through a moving column
of water the phenomenon of an ether-drag is exhibited
and the coefficient of this drag is 1 — 1/+ where p is
the index of refraction of the water. Let us suppose
that v is the velocity of light in still water,, which we
know is connected with the index of refraction by the
formula v=c/p, where c is the speed of light. If, then,
the stream of water moves with the velocity u, we shall
obtain as the total velocity of the light the value
(w+»!/(l+w «/c 3 ) which reduces to w+m( 1 — 1/+)
by neglecting terms containing the reciprocal of the ve-
locity of light. This result is consistent with the classi-
cal theory and, as you can see, is obtained in the simp-
lest manner and without the necessity of making any
assumption whatever about the structure of matter.

EXPERIMENTAL VERIFICATION OF RELATIVITY 109

Astronomical aberration is just as easily explained
on the basis of the relativistic addition of velocities,
but since the mathematical details are somewhat in-
volved the derivation of the formula will be omitted.
It is interesting to observe, however, that the classical
theory and the relativity theory lead to formulas which
differ in terms of second order so that it may be possi-
ble some day to distinguish between them when more
refined instruments are available.

One of the most interesting phenomena in the
theory is the gain of mass experienced by a body when
in motion, a gain which is exactly accounted for by the
theory of relativity. Experiments showing this dif-
ference in mass for various velocities were carried out
by A. H. Bucherer in 1909. Our opponents wish to
reinteipret these results as indicating a change in the
charge rather than a change in the mass of particles
studied. However, upon this point we are all in agree-
ment, that something changes with velocity and since
a change in mass of the desired order is predicted from
the postulates of relativity, the experiment, far from
leading to a contradiction with the theory, must in-
crease our confidence in it.

I turn finally to a consideration of the remarkable
experiments of Professor Miller. I do not expect to
explain them, nor can I feel, after considering the
careful technique employed, that there is a large experi-
mental error in them. Some kind of a disturbance was
found in the ether at the top of Mount Wilson that was
not found at Cleveland. What I do take exception to
is the explanation that this disturbance is due to an
absolute velocity in space since such a conclusion is in

110

A DEBATE ON RELATIVITY

contradiction with the principles of relativity. In sup-
port of this contention I shall first show that the re-
sults of Professor Miller are not in agreement with the
proper motion of the earth as it has been calculated
from a study of the proper motions of the fixed stars. •
Apex der Sonnenbewegung
a <= 270 0 d — 32 0 ® = 20 km/sec

Figure 16

From J. Weber, Pliysikahsche Zcitschrift.

As you are aware the earth turns on its axis once
a day and moves around the sun with an average or-
bital velocity of 18.6 (30 km.) miles per second. In
addition to this the earth shares a motion with the sun
in space which has been estimated to be about 12 miles

EXPERIMENTAL VERIFICATION OF RELATIVITY 111

(20 km.) per second in the direction of the constella-
tion Hercules. (R. A. 270°, 8=32°). You will see
m the diagram of figure 16 13 three vectors with single
arrows which represent the velocities of the earth as

Apes a = 270° <5 + 3*0 Bade Mhrz

Sternzeit
Figure 17.

we know it from a study of the framework of the fixed
stars. The arrows in the ecliptic represent the orbital
velocity of the earth on March 21 and September 23 re-
spectively and the arrow 32° above the equator shows

13 From J Weber: Physikahsche Zeitschrift, vol. 27 (1926)

0 5.

112

A DEBATE ON RELATIVITY

the direction of the velocity of the entire system. If
these two velocities are compounded into a single ve-
locity represented by the double headed arrows, we
find that the velocity of our earth on March 21 is very
close to the plane of the equator and on September 23
is about 65° above the equator. In simple language
this means that the interferometer should show a dif-
ference in the magnitude of the earth’s velocity at dif-
ferent times during the year, a thing Professor Miller
did not find since nearly identical readings were ob-
tained both in September and March. You will see
from Figure 17 (Weber) the discordance between
Miller’s results and the calculated curves both in di-
rection and magnitude. If the earth is moving
through the ether in the direction that we have many
reasons to think it has, then the apparent direction of
the velocity at Mount Wilson should change for every
hour during the day in a regular sinusoidal curve. You
will notice that the azimuth angle in Professor Miller’s
curve is zero at 12 o’clock when as a matter of fact it
should have its maximum value at that time.

In order to meet the difficulty that his observations
do not show a variation with the time of year, Profes-
sor Miller then assumes that we are really moving in a
direction quite different from what we think we are by
referring to the framework of the stars and with a ve-
locity that is much greater. As a matter of fact he
believes that the velocity of the solar system is not 20
km. per second in the direction of the constellation of
Plercules, but is probably more than ten times as great
in the direction of the constellation Draco (R. A. 262°,
h— l 65°). In order to support this assumption Pro-

EXPERIMENTAL VERIFICATION OF RELATIVITY 113

fessor Miller then points out that a velocity of approx-
imately this direction and magnitude is obtained from
a study of the proper motions of the globular clusters.

I should like to point out, however, that if we are bold
enough to refer our coordinate system to the spiral
nebulae we might arrive at the conclusion that we are
moving through space with the incredible velocity of
perhaps 1,000 km. per second. It is this very fact that
there are no “natural axes” in the heavens to which we
can refer our “absolute velocity” except the intangible
wraith of the “fixed ether” that, in my opinion, gives
relativity one of its most powerful arguments. I do
not contend that Professor Miller may not be able to
assign a direction and a magnitude to the velocity of
the earth in space which will be mathematically con-
sistent with his experimental results, but that to talk
of such an “absolute velocity” as having any relation to
the matter of the universe is without meaning.

A second argument seems to show that Professor
Miller has not written finis to the theory of relativity.
This is the contradictory results obtained by Toma-
schek in his repetition of the Trouton and Noble ex-
periment on the Jungfrau to which reference has al-
ready been made. In Miller’s paper on the “Ether-
drift Experiments at Mount Wilson” published in 1925
he makes the statement : “The ether-drift experiments
at Mount Wilson during the last four years, 1921 to
1925, lead to the conclusion that there is a relative mo-
tion of the earth and the ether at this observatory of
approximately nine kilometers per second, being about
one-third the orbital velocity of the earth. By com-
parison with the earlier Cleveland observations, this

114

A DEBATE ON RELATIVITY

suggests a partial drag of the ether by the earth, ivhich
decreases with altitude”. Professor Miller in his re-
port in Science in 1926, however, makes the following
statement which is apparently in contradiction with the
conclusions previously obtained: “The evidence now
indicates that the drift at Mount Wilson does not differ
greatly in magnitude from that at Cleveland and that
at sea-level it would probably have the same value”. If
the latter statement is to be accepted as the final con-
clusion, then it appears that the Michelson-Gale ex-
periment is still in contradiction with the Mount Wil-
son results, if, on the other hand, the ether-drift is af-
fected by altitude, then the results of Tomaschek are
also in contradiction. Tomaschek makes the following
statement on this point: “In case the positive result
of the Michelson interference experiment is confirmed,
the result obtained in this work [The Troulon-Noble
experiment] will mean an entirely new and up to now
wholLy unexpected behavior of the electro-magnetic
field connected with matter, of the lines of force con-
nected on the one hand with the charge and on the
other hand of the field found in light rays.” It ap-
pears, therefore, that we have a conflict -of experi-
mental evidence and until all of the experiments have
been repeated under identical conditions, it seems that
the part of wisdom is to withhold final judgment.

A third argument that seems cogent to me is that
the actual optical properties of the rotating framework
of the earth have not yet been thoroughly investigated
as has already been indicated. The acceleration field
obtained by compounding the orbital velocity of the
earth with its rotation can not be neglected entirely

EXPERIMENTAL VERIFICATION OF RELATIVITY 115

and if to this is added the gravitational field of the
earth, the coefficients of Einstein’s fundamental line
element,

4

ds-= g tj dxi d.Vj ,

»/=l

might be found to differ substantially from those in free
space. Until a further investigation of optical phenom-
ena on the earth is made on the basis of this corrected
line element, the results of the Miller experiment can
not be said to be in contradiction with the theory of
relativity. There are certain small anomalies still ex-
isting in the theory of aberration which makes that sub-
ject one of perennial interest to the astronomer al-
though nearly 200 years have elapsed since it was dis-
covered by Bradley. Miller has suggested that these
might be an indication of a variation in the ether at
different stations on the earth. Until we know. more
about the proper motion of the solar system there is
no reason why we could not explain such variations as
being indications of a hitherto undetected acceleration
of the system.

In conclusion let me state that the succession of
steps by means of which we have arrived at the theory
of relativity tends to increase one’s belief in the valid-
ity of the fundamental postulates. The Maxwell field
equations of electromagnetism are direct mathematical
consequences of the experimental work of Faraday
and Ampere and rest upon the secure foundation of
successful explanation of known phenomena and the
prediction of new. The remarkable fact that these

116

A DEBATE ON RELATIVITY

equations are invaiiant under the Lorentz transfor-
mation is enough, it seems to me, to have led to the re-
stricted theory of relativity even without the experi-
ment of Michelson and Morley. This fact, seldom
sufficiently emphasized, seems to me to be one of great
significance since it came out of the equations long af-
ter their formulation and could not have been put there
by design. The only other fact that seems to me to
compare with it in the history of physical science is the
identification by experiment of the physical constant
which appears in the same equations, with the speed of
light.

THE FOURTH DOCTRINE OF SCIENCE AND
ITS LIMITATIONS

The Rebuttal of the Negative by Professor MacMillan

During the past one hundred years there have arisen
four great doctrines in the scientific world. Curiously
enough two of these doctrines have met with universal
approval among scientific men, while the other two
have met with a violent disapproval.

The first of these great doctrines is the doctrine of
the conservation of energy. Without attempting to
define what energy is, merely recognizing it as the
source of the activities of nature, it is asserted that
energy can be neither created nor destroyed. It changes
its form from potential energy to kinetic energy and
back again, and these changes are the activities of na-
ture, but its total amount is neither increased nor de-
creased. That something should remain constant in
the world of increasing change and flux has an almost
universal appeal to our esthetic sense, and the doctrine
of the conservation of energy commands an almost uni-
versal approval.

The second of these doctrines which enjoys the
hearty assent of the scientifically minded is the doctrine
of evolution. I do not mean evolution in the narrower
sense of biological development, but evolution in the
broader sense of the continuity of the physical universe
throughout all time, and the orderliness of the proc-
esses of change which go on unceasingly. Every physi-

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A DEBATE ON RELATIVITY

cal unit which we recognize in nature, electrons, atoms,
crystals, cells, stars, galaxies, has at some time come
into existence and at some time in the future will pass
out of existence ; and furthermore the manner of their
coming and going is quite orderly, and, within reason-
able limits, is even predictable. No physical unit is
permanent in the sense that it always has existed and
that it will continue to exist throughout all time. Our
sense of permanency is quite satisfied with the doctrine
that energy is constant, and our sense of change also
is satisfied with the doctrine that no physical form en-
dures forever. Like the individuals of the human race,
all of the physical units of nature come and go in un-
ending sequence. The manner in which they come and
go is the subject matter of science, and the intense
scientific activity of the present time is a real measure
of our intellectual curiosity. Our willingness to grant
these two fundamental postulates merely expresses our
readiness to believe that science is possible, and that
the activities of nature are not merely capricious.

In contrast with these two postulates which have
been so favorably received are two other great doc-
trines which have aroused a vast amount of disap-
proval. The first of these is commonly called the sec-
ond law of thermodynamics. It implies that the phys-
ical universe is a mechanism which, like a clock, is
running down. The energy of the universe, notwith-
standing it is constant in amount, is always degenerat-
ing into heat and being radiated away, and is no longer
available for useful work. . Hence if the universe is
to continue indefinitely in its present form, like the
clock it must at some time in the future be wound

THE FOURTH DOCTRINE OF SCIENCE

119

up by some outside agency. If this does not occur
either the universe passes into a state of complete stag-
nation or into some other state in which the physical
units with which we are acquainted no longer exist.

Notwithstanding that such a doctrine is repellent to
our philosophical instincts, it is a doctrine which is ex-
pressible in mathematical form and which can be used
in predicting physical and chemical phenomena. Even
though our esthetic feelings are outraged, it has a
thoroughly reputable standing among scientists, for
in all of their operations they find that the doctrine is
verified. We can not help but wonder why the uni-
verse has not run down long ago, and such a thought
certainly makes us withhold our assent, however useful
the proposition may be in our laboratories. Just as
the universe far transcends our laboratories, so also
must the postulates of our philosophies transcend our
experience. We withhold our assent to this doctrine,
not because it is out of harmony ivith our experience,
for quite the contrary is the case, but because it vio-
lates our esthetic sensibilities.

I have myself had the pleasure of suggesting an
escape from its philosophical implications while still
admitting its validity in the laboratory.. The physicists
have made us acquainted in recent years with the fact
that the atoms are built up of electrons which are of
two types, the positive and negative units of electricity.
In ordinary matter these two kinds of electrons are
numerically equal and therefore ordinary matter is
electrically neutral at ordinary distances. The property
of mass, however, depends upon the existence of elec-
trical fields of electrons. As long as the electrons are

120

A DEBATE ON RELATIVITY

separated, as they actually are in the atom, the electrical
fields exist and the atom possesses the property of
mass. If the organization of the atom is destroyed
and the electron and proton fall together and actually
unite, an enormous amount of energy is liberated, and
the two electrical fields, exactly superimposed, no
longer possess the property of mass. The resulting
physical unit does not have the properties of ordinary
matter. From an astronomical point of view this hy-
pothesis has great merit, for it is the only adequate
hypothesis which we have to account for the vast
amount of energy which the sun and the stars have
radiated into space over the enormous periods of time
which have elapsed since they came into being.

If the atoms are destroyed and consumed in the
fiery interiors of the stars, they are re-formed by the
radiant energy in the quietudes of astronomical space
and it is in this manner that the gaseous nebulae of the
skies come into existence. It is for this reason, too,
that the night skies are cold and black, for the energy
has been absorbed in the manufacture of atoms. I have
not the time now to go into details, but this hypothesis
is very effective in harmonizing our knowledge of
things celestial. It is also very effective in harmoniz-
ing the second law of thermodynamics with a normal
system of philosophical postulates.

The second law of thermodynamics is of the same
type as the statement : “Water always flows down hill”.
Everyone will grant that statement. It is true, but it
is not the whole truth. Water in the liquid form will
flow down hill, but in the form of vapor it is equally
natural for water to rise. One would naturally expect

THE FOURTH DOCTRINE OF SCIENCE

121

some similar statement to apply to energy when it is
locked up in atomic form and the atom is tossed about
by the various forces which it encounters on its way
from its birth place in the depths of astronomical space
to the place of its extinction in the interior of some
star. But like the water when in the state of vapor the
law is reversed when the energy is in the radiant form,
and therefore in the long run there is neither up nor
down. The average is neither way, merely “contin-
ued existence.’’

The second great doctrine which has encountered
disapproval is Einstein’s doctrine of relativity. This
doctrine belongs essentially to the domain of geometry.
It neither adds to nor subtracts from our stock of phys-
ical knowledge. It seeks a re-interpretation of our ex-
perience in the light of a certain type of non-Euclidian
geometry. To one who is not prejudiced against it, but
who seeks merely to see what it can do, it seems to
have had some success in interpreting certain measure-
ments which the discussions of Professor Hufford and
Davis have very ably brought before you. A relativity
enthusiast will assure you that his interpretation is
completely successful. A neutral thinker, however, is
more cautious. In none of the critical experiments
can the success be said to he complete. At best the
success is but partial. You are satisfied, I think, that
the experiments are all very difficult and that it is not
possible for us to say with any precision that is satis-
factory just what the facts are. The individual obser-
vations are singularly discordant and the discrepancies
are too great to make the averages of the observations
highly trustworthy.

122

A DEBATE ON RELATIVITY

Perhaps the most successful prediction is that re-
lating to the perihelion of Mercury. But even here
one remembers that the astronomical values given by
Leverrier and Newcomb depend upon certain discord-
ant residues which remain after a very long and ardu-
ous process of mathematical distillation. These resi-
dues are discordant, probably, because it is impossible
to make observations which are perfect, and so all the
imperfections in the observations of a hundred years,
both of a systematic and of an accidental character,
appear in these residues. They could not be made to
harmonize perfectly by any process whatever except
by the elimination of all of the errors of observation,
and that is out of the question. Time, and improved
observations, alone can tell whether the figures given by
Leverrier and Newcomb represent anything real; and
that quite likely will be a matter of many decades,
even if not a matter of centuries. As the matter stands
at present, however, the agreement between the figures
of Newcomb and Einstein is astonishingly good.

As for the results of the bending of light rays from
stars appearing near the limb of the sun during an
eclipse of the sun by the moon, I believe Professor
Campbell of the Lick Observatory has stated that the
results of the observations agree so well with the pre-
dictions of relativity that the Lick Observatory will
make no further observations along this line. It is im-
possible for me to share with Professor Campbell in
this positive conclusion. The agreement to which he
refers is statistical only. The diagrams which show the
predicted displacements and the observed displacements
are certainly not very similar. Not only do the radial

THE FOURTH DOCTRINE OF SCIENCE

123

displacements differ, when considered individually, but
there are relatively large tangential displacements which
Einstein does not predict at all. The number of stars
considered was less than one hundred, and such a
small number does not give a statistical conclusion
great weight; and particularly is this true when the
predicted displacements and the observed displacements
are, individually, widely discordant.

It is well known that the predicted shift in the lines
of the spectrum of the sun could not, at first, be found.
The best equipment for such observation is un-
doubtedly in the solar observatory at Mount Wilson,
and no observer is more careful and trustworthy than
St. John. For several years he was skeptical about
the predicted shifts. Like all the other critical tests
the matter is very difficult, not because the shift itself
lies beyond the reach of measurements, but because the
lines of the sun are shifted from other causes. Even-
tually, however, a system of corrections was found
which brought the observations and the theory into
accord, and the matter was so announced by St. John.
The agreement between theory and observation was not
a simple one, as in the previous cases. Certain cor-
rections must be applied. The skeptic is rude enough
to suggest that perhaps there are yet other corrections
which should be applied, and that one can never be sure
that the list is complete. These possibilities do not
disturb one who wants to believe, but they are certain
to occur to one who does not.

The dwarf-white companion of Sirius has attracted
much attention of late because it is alleged to be fifty
thousand times as dense as water, or twenty-five hun-

124

A DEBATE ON RELATIVITY

dred times as dense as platinum — approximately one
ton per cubic inch. For such a star the theoretical shift
of the lines of the spectrum is very large. Unfortunate-
ly the star is so dose to the very bi illiant Sirius that it
is hard to get a satisfactory spectrum. Nevertheless
Adams thinks the predicted shift is observable, al-
though he seems to admit some uncertainty.

It would require a great deal of evidence of a very
high character to convince a normal man that a whole
star is twenty-five hundred times as dense as the den-
sest terrestrial substance. The difficulty is much the
same as would be encountered in expecting a lover of
athletic sports to believe that a new athlete had ap-
peared who could jump fifteen thousand feet high, or
one who had extended the record for the running
broad jump from twenty-five feet to twelve miles.
Human credulity does not often take such flights, and
we must admire the strong nerves of the man who puts
forth such startling ideas seriously. He must not ex-
pect us to take it seriously, however, and we can only
smile when he asks us to regard such statements as evi-
dence of anything whatever. Doubtless there is some-
thing peculiar about the companion of Sirius, hut the
evidence is far too feeble to support the extraordinary
conclusion which has been placed upon it.

I come finally to the experiments of Professor
Dayton C. Miller, which are repetitions of the original
Michelson-Morley experiments of a more refined char-
acter and under a greater variety of conditions. There
seems to be little disposition on the part of anyone to
doubt that Professor Miller has actually measured
something. The doubts all rest on the interpretations

THE FOURTH DOCTRINE OF SCIENCE

125

of what he has measured. The relativist, who is com-
mitted to the idea that there is nothing to measure, is
puzzled and is looking around for something he had
not thought of before. He wishes to keep his postu-
lates, and yet find an explanation for the new experi-
ence. That it can be done I have but little doubt, for
I do not think that the differences between the rela-
tivists and the classicists can be decided permanently
by experiment. Miller’s experiment is at least a tem-
porary check to the triumphant march of relativity.
That such a check would be encountered sooner or later
was to have been anticipated, for no formula will ever
prove to be a universal solvent of physical difficulties.

The differences between the relativists and the
classicists lie beyond the reach of experiment. They
are of the same character as the differences between
the Presbyterians and the Baptists. They are postula-
tional only, but inasmuch as the relativists have de-
liberately abandoned the intuitions, which are, so to
speak, the eyes of the intellect, it is impossible to be-
lieve that any large portion of the human race will
follow them into their difficult and dark domain.
Most of us will prefer the open sunshine of our intui-
ion, which undoubtedly is one of the most treasured
inheritances of our race.

Let me conclude my argument by summarizing
briefly the situation as it appears to me. The object of
science is to build up an intellectual system in which
the well verified experiences of the human race are
coordinated and unified and from which suggestions
are derived for the extension of that experience. This
intellectual system is a structure which rests upon a

126

A DEBATE ON RELATIVITY

relatively large number of concepts which cannot be
defined, but which serve as a basis for the definition
of secondary and other subsidiary concepts, and a large
number of postulates which cannot be proved, but
which serve as a basis for the establishment or proof of
other relations which are logically derivable from them
or of hypotheses which make a direct appeal to ex-
perience. These undefined concepts and unproved pos-
tulates are suggested to us by our experiences with
the world about us, but there is nothing absolute or
necessary about them.

Quite likely infinitely many sets of concepts and
postulates are adequate for the interpretation of such
experiences as the race will have, and no one set, in
itself, can claim priority. Nevertheless, owing to the
particular experiences which the race has had and the
order in which these experiences have occurred, our
intuitions have been developed in such a way that the
geometry of Euclid and the mechanics of Newton
seem to be their natural expressions, and non-Euclidean
geometries and non-Newtonian mechanics, while logi-
cally coherent, are essentially unintelligible until their
propositions can be interpreted in terms of Euclid and
Newton. The mechanics of Einstein are non-Newton-
ian in character and make no appeal to our intuitions.
Consequently our intellects, being what they are, will
not be satisfied with an explanation which is incom-
prehensible. They will always cry “Speak to us in a
language which we can understand. We are not satis-
fied with mere formulas.”

For the sake of a very few minute and obscure phe-
nomena the relativists ask us to change the very struc-

THE FOURTH DOCTRINE OF SCIENCE

127

ture of our mental being. Even worse, some of them
are bold enough to assert that we must change, there-
by implying that their system of postulates occupies a
unique position among all possible systems of postu-
lates. There is no assurance as yet that even these
minute phenomena satisfy the claims of the relativists.
The measurements are very difficult, and the errors of
measurement may be several times the magnitude of
the quantity which it is sought to measure. Unless
there is a perfect agreement between the predictions
of relativity and the results of measurement all of the
advantage which its adherents claim is lost and rela-
tivity will be reduced to its proper place of equality
among the postulational systems. And even if the
agreement should turn out to be perfect, the advantage
will be only of a temporary character. In the long run
our geometries and our mechanics will reflect rather
the nature of our intellects than the nature of the uni-
verse which we are trying to understand.

PHILOSOPHICAL IMPLICATIONS OF THE
THEORY

The Final Rejoinder of the Affirmative by Professor
Carmichael.

It is inspiring to come before an audience which is
still alert after listening for two hours to arguments
concerning such minute differences of measurement
as those involved in the crucial tests of relativity. Let
us note how exceedingly small is the shift in the spec-
tral lines of light coming from the sun. We take that
part of the spectrum where the requisite measurements
are most easily made. The length of the shift can be
realized in the following way. Begin with a stick a
meter long. Take one-tenth of it; then take one-tenth
of the small piece thus obtained; then take again one-
tenth of the piece retained ; then again one tenth of
this ; and continue the process for ten consecutive steps.
Playing done this, divide the exceedingly small length
which remains into 125 equal parts and retain one of
these parts. This is the amount of the spectral shift
involved.

It is inspiring to witness that divine curiosity of the
human intellect which compels a general and profound
interest in theories which differ experimentally by such
minute quantities as that just indicated. The human
mind is not satisfied with a theory which is nearly in
agreement with fact. As long as there is the minutest
difference which may be detected by measurement there

PHILOSOPHICAL IMPLICATIONS OF THE THEORY 129

is a struggle forward to arrive at precision of agree-
ment between theory and observation— not because the
small observational difference is a matter of deep con-
cern, but because it is such small differences as these
which enable us to choose between rival philosophies of
science.

It is inspiring, as I said, to see the ardor of interest
on the part of this audience undiminished after two
hours of continuous debating, especially when one re-
members the fact that we have here not merely physi-
cists and mathematicians, who have a professional in-
terest in the subject, but also chemists and biologists
and classicists and business men and, indeed, those
whose main interests are of the most diversified char-
acter. It is a striking witness to the divine curiosity
of the human spirit.

There are three main demands, as we said last
night, which the human spirit will insist upon in the
case of any scientific theory that is a claimant for ac-
ceptance: It must be in suitable agreement with the
facts of nature; it must have those esthetic qualities
which render it pleasing to the human spirit; and it
must furnish what is to us the most agreeable theory
from the point of view of convenience. In the light
of all that has now been said let us reexamine the
theory of relativity with regard to the way in which it
meets this fundamental test.

In making this analysis we shall be guided by the
implications of the following postulate: “A concep-
tion exists for physics only insofar as it is possible to
determine whether it is true or not,” that is, whether it
is consonant with fact. Moreover no basis of physical

130

A DEBATE ON RELATIVITY

science can be considered satisfactory, even as a tem-
porary halting stage, which requires, for its applica-
tion to phenomena within its range, the frequent intro-
duction of ad hoc hypotheses, special hypotheses
brought in to make it possible to find a suitable ex-
planation of phenomena in restricted ranges. This is
a violation of the principle of convenience in physical
theory — a principle whose importance has been insisted
upon by Copernicus and by others since his day. The
use of ad hoc hypotheses is an admission of essential
defects in a theory. It should be insisted upon strongly
that a fundamental theory should be so based that it
is unnecessary to lay temporary or tentative founda-
tions to support important parts of its edifice. The
foundation should be sufficient to carry the whole su-
perstructure of that domain of truth for which it is
suitable. A theory of gravitation does not need to
embrace electromagnetic phenomena, but it is essential
that a theory of gravitation should embrace all gravi-
tational phenomena. Otherwise the theory is distinct-
ly defective.

For this reason we must reject as unsatisfactory
the explanations of the perihelion advance of Mercury,
as accounted for (up to the present) on other bases
than that of the theory of relativity. All such explana-
tions, so far as I am aware, depend upon ad hoc hy-
potheses. If it should turn out — when the matter has
been thoroughly sifted — that there is a real discrepancy
between the theory of relativity and the aberrations
in the motion of the planet Venus, then there would be
a valid objection to the theory of relativity. For some
years I have believed that the whole problem of the

PHILOSOPHICAL IMPLICATIONS OF THE THEORY 131

perihelion advance of the planets should be worked
out anew both theoretically and by analysis of the rec-
ords of observations. This remark applies to the mo-
tion of Mercury as well as that of the other planets.
Until this has been done I do not think that we are
justified in trying to pronounce final judgment on the
matter. The theoretical basis needs to be examined
more rigorously. When this is done the results, as I
anticipate them, will be in favor of relativity.

Owing to the same objection to ad hoc hypothesis, I
think that we should not at present place any great em-
phasis upon the possibility of explaining the fine struc-
ture of the spectrum lines by alternative hypothesis.
But in this case the experiment does not furnish a cru-
cial test of relativity and hence is not decisive one way
or the other. That theie is an explanation on the basis
of the Einstein theory is interesting to the relativist
but he can hardly consider it a matter on which the
theory must stand or fall.

Furthermore these alternative explanations, it ap-
pears to me, are often considered in a false light. They
are sometimes presented as if the existence of an al-
ternative explanation of a phenomenon is in some
sense a blow to relativity. But this is clearly not so, as
any one must see who remembers what we said last
night, on the basis of a proof by Poincare, that if there
is one explanation of a class of physical phenomena
then there is an infinitude of such explanations. Thus
from the existence of an explanation by means of rela-
tivity, one knows in advance that there will be an
infinitude of explanations. Therefore it can not be a
blow to relativity to have one of them pointed out.

132

A DEBATE ON RELATIVITY

The question that needs to be asked is this: Among
these possible explanations which is the most con-
venient and agreeable? On the answer to this ques-
tion turns the decision to be rendered. And the pres-
ence of an ad hoc hypothesis in one of the explanations
is sufficient of itself to damn that one.

We must return once more to the question of simul-
taneity and we must again reject the notion of abso-
lute simultaneity as a scientific conception for the
simple reason that there are no physical means for de-
termining absolute simultaneity. The active past of
an event, or its active future, can be determined by
physical means — by a method which is obvious from
our definition of these conceptions as we gave it last
night. From this we have a physical means of de-
termining what is contemporaneous with a given event,
as we have defined that term. We saw that there
is a certain range within which we must confine what-
ever is to be called simultaneous with an event, using
simultaneity as a conception of physical science. Noth-
ing has been given during the debate to show any more
precise way of approach toward a definition of absolute
simultaneity. The notion that simultaneity is a rela-
tive matter, within the named restrictions, must there-
fore stand as either unchallenged or at least as not
successfully controverted. Perhaps we may then agree
that it has been established that there is a certain
relativity in the conception of simultaneity as an ele-
ment involved in physical science.

If this is accepted, then the classical mechanics
must go, for it is based upon the conception of simul-
taneity as something absolute. Since our opponents

PHILOSOPHICAL IMPLICATIONS OF THE THEORY 133

have shown us no physical means of determining
absolute simultaneity, it seems that even they must
acknowledge this overthrow of the classical mechanics.

There is another conception of simultaneity which
does not belong to physical science but rather to psy-
chology. It is necessaiy to say a few words about
that because the psychological notion of simultaneity
has sometimes been confused with the conception of
simultaneity in physical science. Whatever is present
to a given mental event constitutes a presented simul-
taneity. I may feel a pin prick just as I “see” a dis-
tant star, so that I can not say that either of these
experiences precedes the other. They are together in
the mental event. Psychologically they are simul-
taneous. Yet I may conclude, upon analysis, that the
light which I see left the star a thousand years be-
fore I felt the pin prick, even though the two experi-
ences I have are but parts of one and the same mental
event. It is thus apparent that psychological simul-
taneity is not the same as simultaneity in physical sci-
ence. A confusion of the two has led to a large part
of the difficulty which many people have W'ith the rela-
tivistic conception of simultaneity. These two con-
ceptions of simultaneity are both important and both
deserve the most careful investigation, but only one of
them belongs to the measurable entities of physical
science. As long as people supposed that things happen
when they are seen the confusion of the two was nat-
ural, But the attempt to correlate events as happening
when seen had to be given up when it was observed
that the successive eclipses of Jupiter’s satellites are
seen at shorter intervals when Jupiter and the earth

134

A DEBATE ON RELATIVITY

are approaching each oilier than when they aie reced-
ing from each other. The confusion of the two notions
can now be allowed to stand no longer. Simultaneity
m physical science is relative to a system of reference,
and on such a system it requires physical definition
by means of a technical process.

It is both inconvenient and out of accord with the
facts to try to hold to the notion of absolute simul-
taneity.

If the time permitted, I should like to call to your
minds again those esthetic qualities which are suitable
to render the theory of relativity pleasing to the human
spirit But it would be largely a matter of repetition.
You will have an increasing appreciation of the fact
involved as you become more and more familiar with
the beauty and simplicity and elegance of the funda-
mental principles of relativity, and you can not ap-
preciate it fully until you reach that familiarity. Con-
sequently I shall pass on at once to examine further
the experimental evidence for or against the theory:
for, after all, every theory must stand the fundamental
test of fact.

The three crucial tests have been so analyzed by
my colleague that there is little further to be said about
them. It is admitted that there is a certain room for
difference of opinion about them ; the contrary could
not be successfully maintained before you who have
heard this debate. We can only say that no difficulties
about them have been raised which we had not en-
countered before; and, having examined them in the
light of these difficulties, we are still convinced that the
preponderance of the evidence afforded by them is in

PHILOSOPHICAL IMPLICATIONS OF TIIE THEORY 135

favor of the theory of relativity and that there is no
rival theory, not vitiated by ad hoc hypotheses, which
can approach the theory of relativity in its success in
accounting for them.

Since it is the Miller experiment, more than any
other recent one, which has so given heart to the op-
ponents of the theory of relativity, we must return to
that experiment, even at the risk of repeating some of
the things which were said a while ago by our col-
league. We have no doubt that this experiment is an
important one. Too great care was taken with it for
us to assume that it involves a crude error. The
greatest mistake which we could now make about that
experiment would be to treat it as unimportant. Our
question turns upon the interpretation to be given to
the results.

To begin with let me point out that whatever the
results are they can not afford a direct contradiction
of the principles of relativity as they have been formu-
lated since the appearance of Einstein’s 1916 memoir.
If there is an incompatability between the facts and
the theory it must be brought out by showing that the
facts are out of agreement with some consequences
of the principles; it is only in this indirect way that
such a discrepancy can arise. I hasten to add that it
would be just as fatal to relativity to have it arise
in this way as in any other. My insistence is upon the
proposition that the discrepancy can be shown to exist
only by proving that certain consequences from the
principles as a whole are out of agreement with the
facts. There is no one principle which these facts di-
rectly show to be false. This arises from the limitation

136

A debate on relativity

to free space involved in the statement of the restricted
principle of relativity, while the expeiiment itself was
performed in the presence of a considerable mass of
matter (namely that of the earth) and in a field of
acceleration due to the revolution of the earth on its
axis and to its motion around the sun.

In order to establish a contradiction between the
theory of relativity and the Miller experiment one
would have to find out what effect these fields would
have on the experiment as determined by the theory of
relativity itself. This has never been done, so far as I
know ; certainly our opponents in this debate have made
no claim of having tested the matter in this way. Con-
sequently they have not established a contradiction be-
tween the theory of relativity and the Miller experi-
ment. It is still an open question as to whether there
is a contradiction or not.

In the past it has usually been said that the Michel-
son and Morley experiment is properly accounted for
by the special theory of relativity. Heretofore it has
been assumed that the gravitational field of the earth
is sufficiently small to be negligible even in the case of
the Michelson and Morley experiment ; and it is on the
basis of this hypothesis — which seemed to be justified
by observation — that the special theory of relativity
has been supposed to account for the facts. No one,
so far as I know, has examined this experiment to see
in how far the results would be modified by the actual
gravitational field of the earth, because experiment
seemed to indicate that no such analysis was needed.
Now that we have the additional information afforded
by the Miller experiment — if its results stand the test

rniLOSorincAL implications or the theory 137

of analysis and are corroborated — we may find it
necessary to treat the experiment on the basis of the
general theory of relativity. This would probably
lead, I think, to the conclusion that in the neighbor-
hood of the earth the space-time does not sufficiently
approximate that of free space to justify us in treat-
ing it as such, at least in the case of the Miller ex-
periment. At any rate I feel sure that this is the first
thing for the relativists to test out , as far as I know,
the examination has not been made. Until it has been
made we can not say with certainty what the relation
of the Miller experiment is to the general theory of
relativity.

We have not the time to consider the experimental
evidence further. Since all the available evidence of
this kind has been published there was no chance that
our opponents could confront us with facts which
were unknown to us. All of them we had examined
before and we still remain convinced that none of them
requires us to give up or even to modify the theory of
relativity. We had thought the matter out before
and we still retain our former conclusions and for the
same reasons which had formerly seemed sufficient to
us.

The beautiful lecture delivered by Professor Mac-
Millan last night must now be subjected to analysis.
You can never know beforehand what a brilliant
Scotchman will do ; and so we could not anticipate the
line of argument which we heard last night. To sub-
ject that argument to analysis is a difficult task for me,
since it is hard to know whether it was he or I who
said the most last night in favor of the theory of rela-

138

A DEBATE ON RELATIVITY

tivity. With the general philosophical basis from
which he started I am in, profound agreement. The
only way in which the treatment of natural phenomena
can be made satisfactory is to put it frankly and clear-
ly on a postulational basis, and to bring the postulates
into the clear light of a precise statement. There are
innumerable ways in which these postulates may be
set up. They can not be chosen capriciously, and yet
they are to a large extent arbitrary. There is no
one system which is true while the others all are false.
The different suitable systems merely represent differ-
ent ways in which the postulates may be formulated,
and it is possible to have numerous systems each equal-
ly true. The primary bases of our choice among suit-
able systems must ultimately be that of esthetic satis-
faction and primarily that of convenience. The de-
mand for convenience turns the scale in favor of that
system requiring the fewest ad hoc hypotheses to get
it over its difficulties. The ideal is to have no ad hoc
hypotheses at all. Different people will reach different
conclusions as to which system is most convenient ; and
this is fortunate, since we will then have our scientific
theories approached from many viewpoints.

Professor MacMillan desires to postulate Eu-
clidean space and Newtonian time as the basis of all
physical science. It must be admitted that a conceptual
model of physical phenomena can be built up in this
way. There is an unlimited number of thinkable
time-spaces or systems of separated times and spaces,
and in terms of any of them a conceptual model can be
made to fit the facts.

But in physical science we need to choose among

PHILOSOPHICAL IMPLICATIONS OF THE THEORY 139

these possible models that one or those which meet an
additional requirement. Any model suitable to be re-
tained must be centered around concepts whose agree-
ment or disagreement with facts can be ascertained by
experiment or observation.

Now in the universe of phenomena there are such
things as natural clocks showing the rate at which
time moves in a given small portion of space-time.
Such, for instance, are the atoms of a given structure
situated in different parts of space-time. These de-
termine local time at all places where they are found.
These local times -are the real times. It is a matter of
observation to find out the relations among the relative
rates of these various clocks. To talk about their ab-
solute rate is meaningless, but their relative rates may
be found by observation. In this way it is seen that
they move at different rates in the sense that such a
clock on the sun, for instance, will appear to move more
slowly than one on the earth if it is examined by an
observer from the earth. This is the meaning of the
shift in spectral lines.

Now Newtonian time does not run in this way.
It is therefore not the time actually observed in physi-
cal science. Moreover, Newtonian time postulates an
absolute separation of space and time, whereas in all
our experiences they are so intimately conjoined and
entangled that we can not separate them without muti-
lating them. Thus the facts of physical science enable
us to make a choice among the possible conceptual
models of space and time and to reject certain of them
as not having sufficiently close contact with physical
phenomena. In this way nature appears to rule out as

140

A DEBATE ON RELATIVITY

unnatural, but not impossible, the conception of Eu-
clidean space and Newtonian time as the fundamental
basis of mechanics. The theory of relativity affords
an alternative possibility not subject to this objection.
Its space-time seems to be much closer to that which is
actually indicated by the phenomena of nature.

Some persons find a difficulty in our refusing to
make use of the concept of the ether, and they ask us
what moves and in what medium it moves when we say
that light is propagated with a certain velocity. In the
first place we refuse to employ the concept of an ether
because nobody has been able to assign to it a consist-
ent set of properties for bringing it into agreement with
the necessary facts. Again, we think that the activity
manifested in an event is the fundamental thing and
that the insistence upon the notion of some sort of
metaphysical stuff like the ether only introduces con-
fusion instead of removing the difficulty. It seems that
the ether was invented — you will notice that it was nev-
er observed but was invented — in order to give us a
noun to he the subject of the verb “to undulate”. Let us
not translate such necessities of language into the laws
of physical phenomena. Let us say that a disturbance
moves ; and let us say nothing more, for that is all that
we observe.

I agree with Professor MacMillan in his insis-
tence upon the need of conserving our intuitions as
the basis of our scientific constructs. But I believe
that he has partly confused the intuitional and the
familiar. Some persons are more comfortable in the
presence of Euclidian geometry than with non-Eu-
clidian. But I believe that this is a matter of familiar-

PHILOSOPHICAL IMPLICATIONS OF THE THEORY 141

ity, and not a matter of the fundamental intuitions of
the human spirit. At first the Einstein theory is puz-
zling. As it becomes more familiar it seems to fit our
intuitions better. It appears to me that it will ulti-
mately become more intuitionally comfortable than any
other theory so far proposed.

It is easy to mistake that which is familiar to our
own generation as the thing which conforms precisely
to the fundamental intuitions of the human race. When
this error is avoided and the question of what is in-
tuitional is reduced to a proper analysis and we have
had time to become sufficiently familiar with both
points of view, we shall find, 1 believe, that our in-
tuitions are in favor of the relativistic interpretation
of space-time.

We feel justified in repeating the claim which we
made last night and in recalling to your minds a
promise which we believe we have kept. There is no
experimental fact, tested and corroborated, which is
clearly known to be in contradiction with relativity.
There are facts which have not been brought under its
domain ; we have freely admitted that the theory is noc
ultimate and complete. There are facts which have
been erroneously thought to be in contradiction with it ;
and there are some about which we do not know what
to say at present for lack of sufficient evidence or
analysis. So far as time has permitted we have done,
as promised, one of four things for every presented
fact thought to be in contradiction with relativity: We
have undertaken to show that the charge of contra-
diction has not been convincingly supported : or we
have repelled the charge with convincing evidence ; or

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A DEBATE ON RELATIVITY

we have shown that the facts alleged do not come
within the domain of the present relativity physics ; or
we have analyzed the reasons why the matter should
still be left in the form of an open question. In no
case have we had to allow the established validity ol
the charge, though our weakness has sometimes left
us unable to refute it as forcefully as we would have
wished. We have not been confronted with arguments
of such cogency as to cause us to retreat; perhaps we
are not m the right frame of mind during a debate to
retreat even from an error. But we have tried to be
open to the truth, and we are still convinced that the
great preponderance of evidence is in favor of the
theory of relativity.

As we draw near to the end of this debate we may
assert with emphasis and with confidence, I believe,
that the attack has left the stronghold of relativity un-
shaken. The theory is not perfect; it is not ultimate.
It proceeds in the right direction and its principles and
conclusions must be wrought into every future system
of scientific theory. Changes will be required to
adapt it further to the facts of observation and experi-
ment. It is a growing doctrine, and hence must share
the characteristics of developing theories. But there
is no reason to think that we shall ever go back to the
old ways of thinking.

Its fundamental requirement that only observable
phenomena shall enter into the laws of physical sci-
ence is certain to be met by every enduring theory.
Since it is only relative motions and relative accel-
erations that can be observed, the demand of the old
dynamics for a distinction between relative and abso-

PHILOSOPHICAL IMPLICATIONS OF THE THEORY 143

lute accelerations must be given up in favor of the em-
pirically apparent. “The general theory of relativity
is probably the greatest synthetic achievement of the
human intellect up to the present time.” IL has gained
adherents among the keenest intellects of the genera-
tion in a way which is truly remarkable. It involves
much philosophical doctrine, though it is not based on
this but upon the search for a deep-lying comprehen-
sion of observed facts. It calls clearly for the aban-
donment of metaphysical assumptions in favor of con-
clusions based upon the observable differences in phe-
nomena.

Perhaps its most fundamental insistence upon the
adherence to observed facts lies in its doctrine of the
unification of space and time into the one four-dimen-
sional manifold of space-time. Our conception of this
is doubtless subject to change, but there appears to be
no likelihood that we will again separate them, since
there is no basis in experience for doing so.

The theoiy meets, so far as we can properly judge
at present, all the demands of the supreme test of
adequacy in the case of the phenomena to which it
applies. It is a more convenient theory than any of its
rivals, since it succeeds far better than they in dis-
pensing with ad hoc hypotheses ; it has esthetic quali-
ties suitable to recommend it to the most fastidious hu-
man spirit, once it has become sufficiently familiar to
allow unreasoned prejudice against it to disappear, and
it stands alone in the measure of its success in account-
ing in a fundamental way for the facts of observation
and experience. The contemplation of its beauty and
elegance and the simplicity of its foundations and its

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good success among the phenomena of experience is
enough to produce in one the afflatus of prophecy and
to inspire in him a confidence in its enduring qualities
akin to our certainty of the unchangeableness of the
past. If I were not confronted with the actual ex-
istence of living human beings witnessing to the con-
trary, I would be unable to see how any one properly
acquainted with the theory could fail to be moved with
a profound confidence that it is an advance looking in
the direction which future human thought will take.

Before concluding I wish to speak of the bearing
which relativity has on the general basis of philosophi-
cal thought and on the problem of ethical values.

The theory of relativity has brought us to a new
analysis of the meaning of the customary abstractions
employed in scientific thought and to a new appre-
ciation of their respective roles and their interactions.
It has helped us to see and to realize the implications
of the fact that all abstractions have been developed
from an intuitive phase and that they are subject to the
limitations imposed upon them by their origin. They
can never have a greater validity than the intuitions
from which they have sprung, and they must be sub-
ject to constant revision and extension from the in-
fluence of the intuitions which underlie them. The in-
tuitions back of scientific thought are more fundamen-
tal than the abstractions by means of which that
thought takes explicit and precise form.

You can not fail to see that this conclusion has
wide implications in the matter of ethical and religious
thought. In these fields it is difficult to get far be-
yond the intuitions. There has been a tendency to

PHILOSOPHICAL IMPLICATIONS OF THIS THEORY 145

allow the abstractions of scientific thought to tyrannize
over these intuitions. But when we realize that the
abstractions of scientific thought must be sub j ect, in the
last analysis, to the intuitions underlying science and
that these intuitions have the same character as the
ethical and religious intuitions, we can no longer
consent to have the abstractions of science tyrannize
over ethical and religious intuitions. The latter must
be allowed as great validity as those which underlie
science, and science is under as much obligation to
square with them as with its own underlying intuitions.
For the same reason science can not be allowed to
tyrannize over our social intuitions and the institutions
of society which have grown out of them.

In the development and analysis of the theory of
relativity, and in comparing it with rival theories, one
comes to a clearer understanding of the range of valid-
ity of a particular abstraction and its tendency to be
included in a larger abstraction which replaces it. In
the gradual evolving of codes of conduct we have a
like process of extension and inclusion. “Relativity,”
as Birkhoff says, “does not suggest then that ideals
are relative and shifting, but rather that they will en-
large from time to time.”

The great variety of ways in which an abstraction
can be approached and its multiple relations to the
phenomena from which it arises suggest a new view of
the nature of thought. We see it no longer as an
absolute copy of nature but as a more or less perfect
picture of it ; sometimes we look upon it even as a car-
toon of nature, emphasizing one feature to the point
of distortion. Such is the picture of time afforded by

146

A DEBATE ON RELATIVITY

Newton’s description of it as eternally flowing evenly
independent of space. A realization of this inherent
element of distortion in the nature of a scientific ab-
straction makes for sympathy and tolerance. My
neighbor has as much right to distort it in his direction
as I have to distort it in mine. Two things are re-
quired of us: that we recognize the distortion in our
picture, the partaking of the nature of a cartoon; and
that we strive to remove it insofar as it conflicts with
fact and the demands for esthetic satisfaction and con-
venience.

The historical development of the theory of rela-
tivity, the way in which it has grown out of earlier
theories, has helped us toward a freedom to use an ab-
straction and yet not be enslaved by it. It has made
for tolerance, as is perhaps illustrated by the spirit in
which this debate has been conducted. In particular,
it has struck a blow against the intolerance toward ethi-
cal and religious and social intuitions which has char-
acterized a certain group of scientific workers, and it
has taken the foundations f rom under the materialistic
philosophy which supported them, as we shall presently
show. In so doing it has strengthened the hands of
those more profound and more idealistic scientists
whose science has always allowed a place for the deep-
er values of life and conduct. It is one among the
many forces now making for a return to the more
idealistic conceptions of philosophy, conceptions which
had been obscured for a long time by a false view of
the nature of abstractions in science.

The theory of relativity appears to me to have swept
away the basis of the old materialism in philosophy.

PHILOSOPHICAL IMPLICATIONS OF THE THEORY 147

In this it has been ably supported by many other re-
markable developments of modern physical science —
a science whose achievements in the last thirty years
have been the amazement of all intelligent onlookers,
a science which now has much to say to all natural
sciences about the present outlook and ideals and
norms for scientific progress, a science which is des-
tined to hold such a central position in philosophical
speculation in the next decades as mathematics held in
the past decades.

These influences have swept away the basis of the
old materialism in philosophy. “Matter” is now a
different thing from the matter on which that doctrine
was built. Even the space and the time underlying the
old materialistic theory have given away to a new con-
ception of space-time — a conception marking the radi-
cal return of thought to the basis of experience. The
whole theory of motion has undergone a fundamental
change under the influence of relativity. There is a
natural limit to the velocity of a material body in a
portion of space-time having a given structure. Mass
increases with velocity. There is a mutual interchange
of mass and energy so that the two are but different
aspects of the same thing— a conclusion supported both
by relativity and by many other considerations con-
verging to the same end. Time and space are con-
joined and are inseparably entangled — a fact that is
now to be admitted in thought as well as being found
in all experience. The structure of space-time itself is
modified by the matter in that space-time and by the
motion of that matter. If I wave my hand I change
the structure of space-time in my neighborhood.

148

A DEBATE ON RELATIVITY

The former basis of the old materialism is gone and
that doctrine is now quite impossible It is absurd
to speak of a mechanical explanation of life and
thought when we have found ourselves in such diffi-
culties that we no longer know what we should mean
by a mechanical explanation of phenomena not involv-
ing life.

With no intention or expectation on the part of the
founders that it should be so, the theory of relativity
has become one of the crusaders for the freedom of
the human spirit to follow its deepest and most pro-
found intuitions, and its history has helped to teach
us that science has nothing which can be properly op-
posed to such a freedom. The theory of relativity has
done much to loosen the shackles of the human spirit ;
and, in so doing, it has helped to open the way for a
new evaluation of science and life and thought and a
new understanding of their meaning.

INDEX

152

INDEX

Equivalence, principle of, 28,
56.

Ether, the, 14, 50, 52, 53, 140.

Ether-drag theory, 66-67, 95,
108, 114.

Ether-drift theory, 66-68, 88,
95, 96, 105, 11 3, 114.

Ether wind, (see ether drift
theory).

Euclid, 5, 126.

Euclidean geometry, 43, 61,
138.

Event, definition of an, 11.

Evolution, theory of, 3, 7,
117-118.

External reality, 39.

Faraday, 50, 115
Fictitious time, 53.

Fine structure of spectrum
lines, 106-107.

FitsGcrald, 76.

Fiseau, 67, 68, 88.

Foucault, 91

Foucault’s pendulum experi-
ment 91.

Fresnel, 49, 58, 66, 67, 68.
Fundamental quadratic form,
31-32, SO, 115.

Gale, 87, 93.

Galileo, 49.

Galileo-Newtonian mechanics,
5, 17, 18, 49, 61.

Geometry, Euclidean, 43, 6i,
138; non-Euclideati, 44-47,
62, 121, 126, 140; Lobach-
evski’s, 46, 47, 63 ; Rie-
mann’s, 46, 47, 55.

Gravitation. Einstein’s theory
of, 25-28, 56; Newton’s
theory of, 6, 56, 57, 60,
97; propagation of, 51.

Hercules, constellation of,

111, 112.

Hock, 66.

Huxley, 3.
Iluygliens, 49, 65.

Invariance of nature, 43.

Jupiter, 79, 133.

Kant, 90.

Kauffman, 77.

Kauffman-Buoherer experi-

_ ment, 77-78, 89, 109.

Kelvin, 70.

Kepler’s laws, 57-58, 102.

Laboratory, falling, 25-27.

Larmor, 53.

Law of Science, definition oi»

6 .

Leverrier, 79, 122.

Lcvi-Chita, 56 .

Lick Observatory, 57, 81, 98,
99, 122.

Light, aberration of, 65, 92,
107-109, 115; bending of,
81-83, 99-100) 122; cor-
puscular theory of, 65, 82;
nature of, 49, 65, 82 ; speed
of, 20, 49, 54.

Lobachevski’s geometry, 46,
47, 63.

Local time, 53.

Lorentz-FitzGerald contrac-
tion, 52-53, 76.

Lorerrfz transformation, 18-
19, 22, 53, 116.

Mach, 90.

Mass, longitudinal and trans-
verse, 76 ; rest, 76.

Mass and energy, 55,
Materialism and relativity,
146-148.

INDEX

15.?

Maxwell, SO, 51, 115.

Maxwell equations, invariance
of the, 115.

Mendel's Law, 7.

M idle Ison, 51, 68, 69, 87, 88,
93, 114, 116.

Michelson and Gale Experi-
ment, 87, 92, 93-97, 114.
Michelson and Morley experi-
ment, 13, 51, 52, 54, 60,
68-70, 76, 89, 95, 116, 124,
136.

Miller, D. C ., iii, 2, 14, 70,
71, 72, 74, 75, 88, 89, 95,
97, 106, 109, 110, 112, 113,

114, 115, 124.

Miller experiment, 70-76, 109,

115, 124-125, 135, 136, 137.
Minkmvski, 13.

Morley, 68, 69, 88, 116.

Mount Wilson experiment,
(see Miller experiment).
Mount Wilson observatory,
123.

Natural axes, 113.

Newcomb, 79, 80, 122.
Newton, 49, 58, 59, 65, 108,
126, 146.

Newtonian relativity, 51.
Newtonian time, 43, 49, 53,

61, 80, 138-140, 146.
Newton's laws of motion, 48.
Newton’s theory of gravita-
tion, 6, 56, 57, 60, 97.

Noble, 88, 105, 113, 114.
Non- Euclidean geometry, 44,
47, 62, 121, 126, 140.
Non-Newtonian mechanics, 43,

62, 126.

Noyes, Alfred, 3.

Optical properties of the earth
framework, 96. 114.
Orientation of optical axis in
a moving body, experiment

on, 88, 106.

Parallax, 59.

Perihelion of Mercury, motion
of the, 56, 79, 80, 97-99,
122, 130.

Planck, 82.

Plato, 3.

Poincare, 37, 46, 131.

Poor, 80, 83, 85, 86.

Postulates, nature of, 40-41

Postulates of the physical uni
verse, 42-43.

Postulates of the restricted
theory of relativity, 15-17.

Principia, Newton’s, 59.

Principle of correspondence
of units, 16.

Principle of covariance, 29

Principle of equivalence, 28,
56.

Principle of science, definition
of, 6.

Proper motion of the carfn,
74, 110.

Proton and electron, 120.

Ptolemy, 58, 59.

Quantum theory, 82.

Rayleigh, 88, 106.

Relativity, meaning of term,
5 ; restricted theory of, 5,
13 ; postulates of restricted
theory of. 15-17; Einstein’s
general theory of, 24, 33-
34; Newtonian, 51; physi-
cal postulates of, 93 ; ethi-
cal and religious implica-
tions of, 144-145.

Relativity and materialism,
146-148.

Ricci, 56

Riemann’s geometry, 46, 47,
55.